Low AC resistance conductor designs

ABSTRACT

Described herein are improved configurations for providing a stranded printed circuit board trace comprising, a plurality of conductor layers, a plurality of individual conductor traces on each of the said conductor layers, and a plurality of vias for connecting individual conductor traces on different said conductor layers, the vias located on the outside edges of the stranded trace. The individual conductor traces of each layer may be routed from vias on one side of the stranded printed circuit board trace to vias on the other side in a substantially diagonal direction with respect to the axis of the stranded printed circuit board trace. In embodiments, the stranded printed circuit board trace configuration may be applied to a wireless power transfer system.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.12/639,489, filed Dec. 16, 2009. U.S. application Ser. No. 12/639,489claims the benefit of U.S. App. No. 61/254,559, filed Oct. 23, 2009.

U.S. application Ser. No. 12/639,489 is a continuation-in-part of thefollowing U.S. patent application Ser. No. 12/567,716 filed Sep. 25,2009 which claims the benefit of the following U.S. provisionalapplications, U.S. App. No. 61/100,721 filed Sep. 27, 2008; U.S. App.No. 61/108,743 filed Oct. 27, 2008; U.S. App. No. 61/147,386 filed Jan.26, 2009; U.S. App. No. 61/152,086 filed Feb. 12, 2009; U.S. App. No.61/178,508 filed May 15, 2009; U.S. App. No. 61/182,768 filed Jun. 1,2009; U.S. App. No. 61/121,159 filed Dec. 9, 2008; U.S. App. No.61/142,977 filed Jan. 7, 2009; U.S. App. No. 61/142,885 filed Jan. 6,2009; U.S. App. No. 61/142,796 filed Jan. 6, 2009; U.S. App. No.61/142,889 filed Jan. 6, 2009; U.S. App. No. 61/142,880 filed Jan. 6,2009; U.S. App. No. 61/142,818 filed Jan. 6, 2009; U.S. App. No.61/142,887 filed Jan. 6, 2009; U.S. App. No. 61/156,764 filed Mar. 2,2009; U.S. App. No. 61/143,058 filed Jan. 7, 2009; U.S. App. No.61/152,390 filed Feb. 13, 2009; U.S. App. No. 61/163,695 filed Mar. 26,2009; U.S. App. No. 61/172,633 filed Apr. 24, 2009; U.S. App. No.61/169,240 filed Apr. 14, 2009, U.S. App. No. 61/173,747 filed Apr. 29,2009.

Each of the foregoing applications is incorporated herein by referencein its entirety.

BACKGROUND

1. Field

This disclosure relates to wireless energy transfer, also referred to aswireless power transmission.

2. Description of the Related Art

Energy or power may be transferred wirelessly using a variety of knownradiative, or far-field, and non-radiative, or near-field, techniques.For example, radiative wireless information transfer usinglow-directionality antennas, such as those used in radio and cellularcommunications systems and home computer networks, may be consideredwireless energy transfer. However, this type of radiative transfer isvery inefficient because only a tiny portion of the supplied or radiatedpower, namely, that portion in the direction of, and overlapping with,the receiver is picked up. The vast majority of the power is radiatedaway in all the other directions and lost in free space. Suchinefficient power transfer may be acceptable for data transmission, butis not practical for transferring useful amounts of electrical energyfor the purpose of doing work, such as for powering or chargingelectrical devices. One way to improve the transfer efficiency of someradiative energy transfer schemes is to use directional antennas toconfine and preferentially direct the radiated energy towards areceiver. However, these directed radiation schemes may require anuninterruptible line-of-sight and potentially complicated tracking andsteering mechanisms in the case of mobile transmitters and/or receivers.In addition, such schemes may pose hazards to objects or people thatcross or intersect the beam when modest to high amounts of power arebeing transmitted. A known non-radiative, or near-field, wireless energytransfer scheme, often referred to as either induction or traditionalinduction, does not (intentionally) radiate power, but uses anoscillating current passing through a primary coil, to generate anoscillating magnetic near-field that induces currents in a near-byreceiving or secondary coil. Traditional induction schemes havedemonstrated the transmission of modest to large amounts of power,however only over very short distances, and with very small offsettolerances between the primary power supply unit and the secondaryreceiver unit. Electric transformers and proximity chargers are examplesof devices that utilize this known short range, near-field energytransfer scheme.

Therefore a need exists for a wireless power transfer scheme that iscapable of transferring useful amounts of electrical power overmid-range distances or alignment offsets. Such a wireless power transferscheme should enable useful energy transfer over greater distances andalignment offsets than those realized with traditional inductionschemes, but without the limitations and risks inherent in radiativetransmission schemes.

SUMMARY

There is disclosed herein a non-radiative or near-field wireless energytransfer scheme that is capable of transmitting useful amounts of powerover mid-range distances and alignment offsets. This inventive techniqueuses coupled electromagnetic resonators with long-lived oscillatoryresonant modes to transfer power from a power supply to a power drain.The technique is general and may be applied to a wide range ofresonators, even where the specific examples disclosed herein relate toelectromagnetic resonators. If the resonators are designed such that theenergy stored by the electric field is primarily confined within thestructure and that the energy stored by the magnetic field is primarilyin the region surrounding the resonator. Then, the energy exchange ismediated primarily by the resonant magnetic near-field. These types ofresonators may be referred to as magnetic resonators. If the resonatorsare designed such that the energy stored by the magnetic field isprimarily confined within the structure and that the energy stored bythe electric field is primarily in the region surrounding the resonator.Then, the energy exchange is mediated primarily by the resonant electricnear-field. These types of resonators may be referred to as electricresonators. Either type of resonator may also be referred to as anelectromagnetic resonator. Both types of resonators are disclosedherein.

The omni-directional but stationary (non-lossy) nature of thenear-fields of the resonators we disclose enables efficient wirelessenergy transfer over mid-range distances, over a wide range ofdirections and resonator orientations, suitable for charging, powering,or simultaneously powering and charging a variety of electronic devices.As a result, a system may have a wide variety of possible applicationswhere a first resonator, connected to a power source, is in onelocation, and a second resonator, potentially connected toelectrical/electronic devices, batteries, powering or charging circuits,and the like, is at a second location, and where the distance from thefirst resonator to the second resonator is on the order of centimetersto meters. For example, a first resonator connected to the wiredelectricity grid could be placed on the ceiling of a room, while otherresonators connected to devices, such as robots, vehicles, computers,communication devices, medical devices, and the like, move about withinthe room, and where these devices are constantly or intermittentlyreceiving power wirelessly from the source resonator. From this oneexample, one can imagine many applications where the systems and methodsdisclosed herein could provide wireless power across mid-rangedistances, including consumer electronics, industrial applications,infrastructure power and lighting, transportation vehicles, electronicgames, military applications, and the like.

Energy exchange between two electromagnetic resonators can be optimizedwhen the resonators are tuned to substantially the same frequency andwhen the losses in the system are minimal. Wireless energy transfersystems may be designed so that the “coupling-time” between resonatorsis much shorter than the resonators' “loss-times”. Therefore, thesystems and methods described herein may utilize high quality factor(high-Q) resonators with low intrinsic-loss rates. In addition, thesystems and methods described herein may use sub-wavelength resonatorswith near-fields that extend significantly longer than thecharacteristic sizes of the resonators, so that the near-fields of theresonators that exchange energy overlap at mid-range distances. This isa regime of operation that has not been practiced before and thatdiffers significantly from traditional induction designs.

It is important to appreciate the difference between the high-Q magneticresonator scheme disclosed here and the known close-range or proximityinductive schemes, namely, that those known schemes do notconventionally utilize high-Q resonators. Using coupled-mode theory(CMT), (see, for example, Waves and Fields in Optoelectronics, H. A.Haus, Prentice Hall, 1984), one may show that a high-Qresonator-coupling mechanism can enable orders of magnitude moreefficient power delivery between resonators spaced by mid-rangedistances than is enabled by traditional inductive schemes. Coupledhigh-Q resonators have demonstrated efficient energy transfer overmid-range distances and improved efficiencies and offset tolerances inshort range energy transfer applications.

The systems and methods described herein may provide for near-fieldwireless energy transfer via strongly coupled high-Q resonators, atechnique with the potential to transfer power levels from picowatts tokilowatts, safely, and over distances much larger than have beenachieved using traditional induction techniques. Efficient energytransfer may be realized for a variety of general systems of stronglycoupled resonators, such as systems of strongly coupled acousticresonators, nuclear resonators, mechanical resonators, and the like, asoriginally described by researchers at M.I.T. in their publications,“Efficient wireless non-radiative mid-range energy transfer”, Annals ofPhysics, vol. 323, Issue 1, p. 34 (2008) and “Wireless Power Transfervia Strongly Coupled Magnetic Resonances”, Science, vol. 317, no. 5834,p. 83, (2007). Disclosed herein are electromagnetic resonators andsystems of coupled electromagnetic resonators, also referred to morespecifically as coupled magnetic resonators and coupled electricresonators, with operating frequencies below 10 GHz.

This disclosure describes wireless energy transfer technologies, alsoreferred to as wireless power transmission technologies. Throughout thisdisclosure, we may use the terms wireless energy transfer, wirelesspower transfer, wireless power transmission, and the like,interchangeably. We may refer to supplying energy or power from asource, an AC or DC source, a battery, a source resonator, a powersupply, a generator, a solar panel, and thermal collector, and the like,to a device, a remote device, to multiple remote devices, to a deviceresonator or resonators, and the like. We may describe intermediateresonators that extend the range of the wireless energy transfer systemby allowing energy to hop, transfer through, be temporarily stored, bepartially dissipated, or for the transfer to be mediated in any way,from a source resonator to any combination of other device andintermediate resonators, so that energy transfer networks, or strings,or extended paths may be realized. Device resonators may receive energyfrom a source resonator, convert a portion of that energy to electricpower for powering or charging a device, and simultaneously pass aportion of the received energy onto other device or mobile deviceresonators. Energy may be transferred from a source resonator tomultiple device resonators, significantly extending the distance overwhich energy may be wirelessly transferred. The wireless powertransmission systems may be implemented using a variety of systemarchitectures and resonator designs. The systems may include a singlesource or multiple sources transmitting power to a single device ormultiple devices. The resonators may be designed to be source or deviceresonators, or they may be designed to be repeaters. In some cases, aresonator may be a device and source resonator simultaneously, or it maybe switched from operating as a source to operating as a device or arepeater. One skilled in the art will understand that a variety ofsystem architectures may be supported by the wide range of resonatordesigns and functionalities described in this application.

In the wireless energy transfer systems we describe, remote devices maybe powered directly, using the wirelessly supplied power or energy, orthe devices may be coupled to an energy storage unit such as a battery,a super-capacitor, an ultra-capacitor, or the like (or other kind ofpower drain), where the energy storage unit may be charged or re-chargedwirelessly, and/or where the wireless power transfer mechanism is simplysupplementary to the main power source of the device. The devices may bepowered by hybrid battery/energy storage devices such as batteries withintegrated storage capacitors and the like. Furthermore, novel batteryand energy storage devices may be designed to take advantage of theoperational improvements enabled by wireless power transmission systems.

Other power management scenarios include using wirelessly supplied powerto recharge batteries or charge energy storage units while the devicesthey power are turned off, in an idle state, in a sleep mode, and thelike. Batteries or energy storage units may be charged or recharged athigh (fast) or low (slow) rates. Batteries or energy storage units maybe trickle charged or float charged. Multiple devices may be charged orpowered simultaneously in parallel or power delivery to multiple devicesmay be serialized such that one or more devices receive power for aperiod of time after which other power delivery is switched to otherdevices. Multiple devices may share power from one or more sources withone or more other devices either simultaneously, or in a timemultiplexed manner, or in a frequency multiplexed manner, or in aspatially multiplexed manner, or in an orientation multiplexed manner,or in any combination of time and frequency and spatial and orientationmultiplexing. Multiple devices may share power with each other, with atleast one device being reconfigured continuously, intermittently,periodically, occasionally, or temporarily, to operate as wireless powersources. It would be understood by one of ordinary skill in the art thatthere are a variety of ways to power and/or charge devices, and thevariety of ways could be applied to the technologies and applicationsdescribed herein.

Wireless energy transfer has a variety of possible applicationsincluding for example, placing a source (e.g. one connected to the wiredelectricity grid) on the ceiling, under the floor, or in the walls of aroom, while devices such as robots, vehicles, computers, PDAs or similarare placed or move freely within the room. Other applications mayinclude powering or recharging electric-engine vehicles, such as busesand/or hybrid cars and medical devices, such as wearable or implantabledevices. Additional example applications include the ability to power orrecharge autonomous electronics (e.g. laptops, cell-phones, portablemusic players, household robots, GPS navigation systems, displays, etc),sensors, industrial and manufacturing equipment, medical devices andmonitors, home appliances and tools (e.g. lights, fans, drills, saws,heaters, displays, televisions, counter-top appliances, etc.), militarydevices, heated or illuminated clothing, communications and navigationequipment, including equipment built into vehicles, clothing andprotective-wear such as helmets, body armor and vests, and the like, andthe ability to transmit power to physically isolated devices such as toimplanted medical devices, to hidden, buried, implanted or embeddedsensors or tags, to and/or from roof-top solar panels to indoordistribution panels, and the like.

In one aspect, disclosed herein is a system including a source resonatorhaving a Q-factor Q₁ and a characteristic size_(x1), coupled to a powergenerator with direct electrical connections; and a second resonatorhaving a Q-factor Q₂ and a characteristic size x₂, coupled to a loadwith direct electrical connections, and located a distance D from thesource resonator, wherein the source resonator and the second resonatorare coupled to exchange energy wirelessly among the source resonator andthe second resonator in order to transmit power from the power generatorto the load, and wherein √{square root over (Q₁Q₂)} is greater than 100.

Q₁ may be greater than 100 and Q₂ may be less than 100. Q₁ may begreater than 100 and Q₂ may be greater than 100. A useful energyexchange may be maintained over an operating distance from 0 to D, whereD is larger than the smaller of x₁ and x₂. At least one of the sourceresonator and the second resonator may be a coil of at least one turn ofa conducting material connected to a first network of capacitors. Thefirst network of capacitors may include at least one tunable capacitor.The direct electrical connections of at least one of the sourceresonator to the ground terminal of the power generator and the secondresonator to the ground terminal of the load may be made at a point onan axis of electrical symmetry of the first network of capacitors. Thefirst network of capacitors may include at least one tunablebutterfly-type capacitor, wherein the direct electrical connection tothe ground terminal is made on a center terminal of the at least onetunable butterfly-type capacitor. The direct electrical connection of atleast one of the source resonator to the power generator and the secondresonator to the load may be made via a second network of capacitors,wherein the first network of capacitors and the second network ofcapacitors form an impedance matching network. The impedance matchingnetwork may be designed to match the coil to a characteristic impedanceof the power generator or the load at a driving frequency of the powergenerator.

At least one of the first network of capacitors and the second networkof capacitors may include at least one tunable capacitor. The firstnetwork of capacitors and the second network of capacitors may beadjustable to change an impedance of the impedance matching network at adriving frequency of the power generator. The first network ofcapacitors and the second network of capacitors may be adjustable tomatch the coil to the characteristic impedance of the power generator orthe load at a driving frequency of the power generator. At least one ofthe first network of capacitors and the second network of capacitors mayinclude at least one fixed capacitor that reduces a voltage across theat least one tunable capacitor. The direct electrical connections of atleast one of the source resonator to the power generator and the secondresonator to the load may be configured to substantially preserve aresonant mode. At least one of the source resonator and the secondresonator may be a tunable resonator. The source resonator may bephysically separated from the power generator and the second resonatormay be physically separated from the load. The second resonator may becoupled to a power conversion circuit to deliver DC power to the load.The second resonator may be coupled to a power conversion circuit todeliver AC power to the load. The second resonator may be coupled to apower conversion circuit to deliver both AC and DC power to the load.The second resonator may be coupled to a power conversion circuit todeliver power to a plurality of loads.

In another aspect, a system disclosed herein includes a source resonatorhaving a Q-factor Q₁ and a characteristic size x₁, and a secondresonator having a Q-factor Q₂ and a characteristic size x₂, and locateda distance D from the source resonator; wherein the source resonator andthe second resonator are coupled to exchange energy wirelessly among thesource resonator and the second resonator; and wherein √{square rootover (Q₁Q₂)} is greater than 100, and wherein at least one of theresonators is enclosed in a low loss tangent material.

In another aspect, a system disclosed herein includes a source resonatorhaving a Q-factor Q₁ and a characteristic size x₁, and a secondresonator having a Q-factor Q₂ and a characteristic size x₂, and locateda distance D from the source resonator; wherein the source resonator andthe second resonator are coupled to exchange energy wirelessly among thesource resonator and the second resonator, and wherein √{square rootover (Q₁Q₂)} is greater than 100; and wherein at least one of theresonators includes a coil of a plurality of turns of a conductingmaterial connected to a network of capacitors, wherein the plurality ofturns are in a common plane, and wherein a characteristic thickness ofthe at least one of the resonators is much less than a characteristicsize of the at least one of the resonators.

In embodiments, the present invention may provide a stranded printedcircuit board trace comprising, a plurality of conductor layers, aplurality of individual conductor traces on each of the said conductorlayers, and a plurality of vias for connecting individual conductortraces on different said conductor layers, the vias located on theoutside edges of the stranded trace. The individual conductor traces ofeach layer may be routed from vias on one side of the stranded printedcircuit board trace to vias on the other side in a substantiallydiagonal direction with respect to the axis of the stranded printedcircuit board trace. In embodiments, the number of conductor layers maybe even. The conductor layers may be separated by insulating layers.Each via may connect at least two of the said conductor layers. Theindividual conductor traces on each conductor layer may connect at leasttwo different vias that connect the layer of the individual conductortrace and at least one other layer. The individual conductor traces oneach conductor layer may be substantially parallel to each other. Theindividual conductor traces on adjacent conductor layers may besubstantially orthogonal to each other. The vias may be through vias.The stranded trace may be shaped to form at least one loop. A network ofelectrical components may be coupled to the conductor traces. Theelectrical components may include any of a combination of inductors andcapacitors. The said loops and electrical components of the strandedtrace may form a magnetic resonator. The quality factor of the resonatormay be at least 100. The trace may be part of a wireless power transfersystem.

In embodiments, the present invention may provide for a printed circuitboard magnetic resonator comprising, a plurality of conductor layerswith a plurality of conductor traces on each of the said conductorlayers, a plurality of vias for connecting conductor traces on differentsaid conductor layers, a network of electrical components. The conductortraces may be routed between said vias as to braid the said conductorthrough the conductor layers in a predetermined pattern, thepredetermined pattern of conductor traces and the vias may be shaped asto form at least one loop, and the network of electrical components maybe coupled to the conductor traces. In embodiments, the network ofelectrical components may comprise capacitors. The network of electricalcomponents comprises inductors. Further, the present invention maycomprise a magnetic core, where the magnetic core may be located on oneside of the printed circuit board magnetic resonator, where theconductor's traces spiral around the magnetic core, and the like. Thecapacitors of the network of capacitors may be variable. The network ofelectrical components may be integrated into the printed circuit board.The resonant frequency of the resonator may be less than 1 GHz. Further,the present invention may comprise a power source where the power sourceis coupled to the resonator and drives the resonator at substantiallythe resonant frequency of the resonator. The resonator may be part of awireless power transfer system. The quality factor of the resonator maybe larger than 100. The dimensions of the conductor traces may beoptimized to maximize the quality factor of the resonator.

In embodiments, the present invention may provide for a stranded printedcircuit board conductor coil comprising, a plurality of conductorlayers, a plurality of conductor traces on each of the said conductorlayers, and a plurality types of vias for connecting conductor traces ondifferent said conductor layers, the vias located on the outside edgesof the stranded conductor. The conductor traces of each layer may berouted from vias on one side of the stranded printed circuit boardconductor to vias on the other side in a substantially diagonaldirection with respect to the axis of the stranded printed circuit boardconductor. The printed circuit board conductor may be shaped to form atleast one loop, and adjacent strands of stranded printed circuit boardconductor may share the interspacing of adjacent vias. The adjacent rowsof vias of adjacent stranded conductors may share the same verticallocation and may be stacked one on top of other. The adjacent rows ofvias of adjacent stranded conductors may be separate and equallyinterspersed.

In embodiments, the present invention may include a plurality ofconductor layers arranged into a printed circuit board; a plurality ofindividual conductor traces on each one of the plurality of conductorlayers; and a plurality of vias that connect individual ones of theplurality of conductor traces on different ones of the plurality ofconductor layers into a stranded trace, the plurality of vias located onone or more outside edges of the stranded trace; wherein the pluralityof individual conductor traces on each layer are routed from a firstgroup of the plurality of vias on a first edge of the stranded trace ina plane of the printed circuit board to a second group of the pluralityof vias on a second edge of the stranded trace in a plane of the printedcircuit board in a substantially diagonal direction with respect to thefirst edge of the stranded trace.

The plurality of conductor layers may be an even number of conductorlayers. Two or more of the plurality of conductor layers may beseparated by an insulating layer. Each one of the plurality of vias mayconnect at least two of the plurality of conductor layers. The pluralityof individual conductor traces on at least one of the plurality ofconductor layers may each connect two different ones of the plurality ofvias. Each one of the plurality of individual conductor traces on eachone of the plurality of conductor layers may be substantially parallelto each other one of the plurality of individual conductor traces onthat one of the plurality of conductor layers. Each one of the pluralityof individual conductor traces on each one of the plurality of conductorlayers may be orthogonal to each one of the plurality of the individualconductor traces on an adjacent one of the plurality of conductorlayers. The vias may be through vias.

The stranded trace may be shaped to form at least one loop. A network ofelectrical components may be coupled to the plurality of individualconductor traces. The network of electrical components may include atleast one of an inductor and a capacitor. The at least one loop and thenetwork of electrical components may form a magnetic resonator. Aquality factor of the resonator may be at least one hundred. Thestranded trace may be a part of a wireless power transfer system.

In embodiments, a magnetic resonator disclosed herein may include aplurality of conductor layers in a printed circuit board with aplurality of conductor traces on each one of the plurality of conductorlayers; a plurality of vias that connect different ones of the pluralityof conductor traces on different ones of the plurality of conductorlayers; and a network of electrical components coupled to the pluralityof conductor traces; wherein the plurality of conductor traces arerouted between said vias to braid the plurality of conductor traces intoa predetermined pattern of overlapping conductor traces, wherein thepredetermined pattern is formed into at least one loop.

The network of electrical components may include one or more capacitors.At least one of the one or more capacitors may be a variable capacitor.

The network of electrical components may include one or more inductors.Further including a magnetic core may be located on one side of theprinted circuit board. Further including a magnetic core, wherein theplurality of conductor traces may spiral around the magnetic core. Thenetwork of electrical components may be integrated into the printedcircuit board.

The magnetic resonator may have a resonant frequency of less than 1 GHz.Further including a power source coupled to the magnetic resonator, thepower source may be adapted to drive the magnetic resonator atsubstantially the resonant frequency. The magnetic resonator may be acomponent of a wireless power transfer system. The magnetic resonatormay have a quality factor larger than one hundred.

The plurality of conductor traces may have one or more physicaldimensions selected to optimize a quality factor of the resonator.

In embodiments, a stranded conductor coil disclosed herein may include aplurality of conductor layers in a printed circuit board; a plurality ofconductor traces on each one of the plurality of conductor layers; and aplurality of vias arranged into two or more rows of vias that connectconductor traces on different ones of the plurality of conductor layersto form a first stranded conductor and a second stranded conductor,wherein at least one of the plurality of conductor traces has a paththat is substantially diagonal to at least one of the two or more rowsof vias, and wherein the first stranded conductor and the secondstranded conductor share an area bounded by one of the two or more rowsof vias on one of the plurality of conductor layers.

The path may be substantially diagonal to an edge of the printed circuitboard. All of the conductor traces in at least one of the first strandedconductor and the second stranded may be substantially diagonal to atleast one of the two or more rows of vias.

Throughout this disclosure we may refer to the certain circuitcomponents such as capacitors, inductors, resistors, diodes, switchesand the like as circuit components or elements. We may also refer toseries and parallel combinations of these components as elements,networks, topologies, circuits, and the like. We may describecombinations of capacitors, diodes, varactors, transistors, and/orswitches as adjustable impedance networks, tuning networks, matchingnetworks, adjusting elements, and the like. We may also refer to“self-resonant” objects that have both capacitance, and inductancedistributed (or partially distributed, as opposed to solely lumped)throughout the entire object. It would be understood by one of ordinaryskill in the art that adjusting and controlling variable componentswithin a circuit or network may adjust the performance of that circuitor network and that those adjustments may be described generally astuning, adjusting, matching, correcting, and the like. Other methods totune or adjust the operating point of the wireless power transfer systemmay be used alone, or in addition to adjusting tunable components suchas inductors and capacitors, or banks of inductors and capacitors.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this disclosure belongs. In case of conflict withpublications, patent applications, patents, and other referencesmentioned or incorporated herein by reference, the presentspecification, including definitions, will control.

Any of the features described above may be used, alone or incombination, without departing from the scope of this disclosure. Otherfeatures, objects, and advantages of the systems and methods disclosedherein will be apparent from the following detailed description andfigures.

BRIEF DESCRIPTION OF FIGURES

FIGS. 1 (a) and (b) depict exemplary wireless power systems containing asource resonator 1 and device resonator 2 separated by a distance D.

FIG. 2 shows an exemplary resonator labeled according to the labelingconvention described in this disclosure. Note that there are noextraneous objects or additional resonators shown in the vicinity ofresonator 1.

FIG. 3 shows an exemplary resonator in the presence of a “loading”object, labeled according to the labeling convention described in thisdisclosure.

FIG. 4 shows an exemplary resonator in the presence of a “perturbing”object, labeled according to the labeling convention described in thisdisclosure.

FIG. 5 shows a plot of efficiency, η, vs. strong coupling factor,U=κ/√{square root over (Γ_(s)Γ_(d))}=k√{square root over (Q_(s)Q_(d))}.

FIG. 6 (a) shows a circuit diagram of one example of a resonator (b)shows a diagram of one example of a capacitively-loaded inductor loopmagnetic resonator, (c) shows a drawing of a self-resonant coil withdistributed capacitance and inductance, (d) shows a simplified drawingof the electric and magnetic field lines associated with an exemplarymagnetic resonator of the current disclosure, and (e) shows a diagram ofone example of an electric resonator.

FIG. 7 shows a plot of the “quality factor”, Q (solid line), as afunction of frequency, of an exemplary resonator that may be used forwireless power transmission at MHz frequencies. The absorptive Q (dashedline) increases with frequency, while the radiative Q (dotted line)decreases with frequency, thus leading the overall Q to peak at aparticular frequency.

FIG. 8 shows a drawing of a resonator structure with its characteristicsize, thickness and width indicated.

FIGS. 9 (a) and (b) show drawings of exemplary inductive loop elements.

FIGS. 10 (a) and (b) show two examples of trace structures formed onprinted circuit boards and used to realize the inductive element inmagnetic resonator structures.

FIG. 11 (a) shows a perspective view diagram of a planar magneticresonator, (b) shows a perspective view diagram of a two planar magneticresonator with various geometries, and c) shows is a perspective viewdiagram of a two planar magnetic resonators separated by a distance D.

FIG. 12 is a perspective view of an example of a planar magneticresonator.

FIG. 13 is a perspective view of a planar magnetic resonator arrangementwith a circular resonator coil.

FIG. 14 is a perspective view of an active area of a planar magneticresonator.

FIG. 15 is a perspective view of an application of the wireless powertransfer system with a source at the center of a table powering severaldevices placed around the source.

FIG. 16( a) shows a 3D finite element model of a copper and magneticmaterial structure driven by a square loop of current around the chokepoint at its center. In this example, a structure may be composed of twoboxes made of a conducting material such as copper, covered by a layerof magnetic material, and connected by a block of magnetic material. Theinside of the two conducting boxes in this example would be shieldedfrom AC electromagnetic fields generated outside the boxes and may houselossy objects that might lower the Q of the resonator or sensitivecomponents that might be adversely affected by the AC electromagneticfields. Also shown are the calculated magnetic field streamlinesgenerated by this structure, indicating that the magnetic field linestend to follow the lower reluctance path in the magnetic material. FIG.16( b) shows interaction, as indicated by the calculated magnetic fieldstreamlines, between two identical structures as shown in (a). Becauseof symmetry, and to reduce computational complexity, only one half ofthe system is modeled (but the computation assumes the symmetricalarrangement of the other half).

FIG. 17 shows an equivalent circuit representation of a magneticresonator including a conducting wire wrapped N times around astructure, possibly containing magnetically permeable material. Theinductance is realized using conducting loops wrapped around a structurecomprising a magnetic material and the resistors represent lossmechanisms in the system (R_(wire) for resistive losses in the loop,R_(μ) denoting the equivalent series resistance of the structuresurrounded by the loop). Losses may be minimized to realize high-Qresonators.

FIG. 18 shows a Finite Element Method (FEM) simulation of two highconductivity surfaces above and below a disk composed of lossydielectric material, in an external magnetic field of frequency 6.78MHz. Note that the magnetic field was uniform before the disk andconducting materials were introduced to the simulated environment. Thissimulation is performed in cylindrical coordinates. The image isazimuthally symmetric around the r=0 axis. The lossy dielectric disk has∈_(r)=1 and σ=10 S/m.

FIG. 19 shows a drawing of a magnetic resonator with a lossy object inits vicinity completely covered by a high-conductivity surface.

FIG. 20 shows a drawing of a magnetic resonator with a lossy object inits vicinity partially covered by a high-conductivity surface.

FIG. 21 shows a drawing of a magnetic resonator with a lossy object inits vicinity placed on top of a high-conductivity surface.

FIG. 22 shows a diagram of a completely wireless projector.

FIG. 23 shows the magnitude of the electric and magnetic fields along aline that contains the diameter of the circular loop inductor and alongthe axis of the loop inductor.

FIG. 24 shows a drawing of a magnetic resonator and its enclosure alongwith a necessary but lossy object placed either (a) in the corner of theenclosure, as far away from the resonator structure as possible or (b)in the center of the surface enclosed by the inductive element in themagnetic resonator.

FIG. 25 shows a drawing of a magnetic resonator with a high-conductivitysurface above it and a lossy object, which may be brought into thevicinity of the resonator, but above the high-conductivity sheet.

FIG. 26( a) shows an axially symmetric FEM simulation of a thinconducting (copper) cylinder or disk (20 cm in diameter, 2 cm in height)exposed to an initially uniform, externally applied magnetic field (grayflux lines) along the z-axis. The axis of symmetry is at r=0. Themagnetic streamlines shown originate at z=−∞, where they are spaced fromr=3 cm to r=10 cm in intervals of 1 cm. The axes scales are in meters.FIG. 26 (b) shows the same structure and externally applied field as in(a), except that the conducting cylinder has been modified to include a0.25 mm layer of magnetic material (not visible) with μ_(r)′=40, on itsoutside surface. Note that the magnetic streamlines are deflected awayfrom the cylinder significantly less than in (a).

FIG. 27 shows an axi-symmetric view of a variation based on the systemshown in FIG. 26. Only one surface of the lossy material is covered by alayered structure of copper and magnetic materials. The inductor loop isplaced on the side of the copper and magnetic material structureopposite to the lossy material as shown.

FIG. 28 (a) depicts a general topology of a matching circuit includingan indirect coupling to a high-Q inductive element.

FIG. 28 (b) shows a block diagram of a magnetic resonator that includesa conductor loop inductor and a tunable impedance network. Physicalelectrical connections to this resonator may be made to the terminalconnections.

FIG. 28 (c) depicts a general topology of a matching circuit directlycoupled to a high-Q inductive element.

FIG. 28 (d) depicts a general topology of a symmetric matching circuitdirectly coupled to a high-Q inductive element and drivenanti-symmetrically (balanced drive).

FIG. 28 (e) depicts a general topology of a matching circuit directlycoupled to a high-Q inductive element and connected to ground at a pointof symmetry of the main resonator (unbalanced drive).

FIGS. 29( a) and 29(b) depict two topologies of matching circuitstransformer-coupled (i.e. indirectly or inductively) to a high-Qinductive element. The highlighted portion of the Smith chart in (c)depicts the complex impedances (arising from L and R of the inductiveelement) that may be matched to an arbitrary real impedance Z₀ by thetopology of FIG. 31( b) in the case ωL₂=1/ωC₂.

FIGS. 30( a),(b),(c),(d),(e),(f) depict six topologies of matchingcircuits directly coupled to a high-Q inductive element and includingcapacitors in series with Z₀. The topologies shown in FIGS. 30(a),(b),(c) are driven with a common-mode signal at the input terminals,while the topologies shown in FIGS. 30( d),(e),(f) are symmetric andreceive a balanced drive. The highlighted portion of the Smith chart in30(g) depicts the complex impedances that may be matched by thesetopologies. FIGS. 30( h),(i),(j),(k),(l),(m) depict six topologies ofmatching circuits directly coupled to a high-Q inductive element andincluding inductors in series with Z₀.

FIGS. 31( a),(b),(c) depict three topologies of matching circuitsdirectly coupled to a high-Q inductive element and including capacitorsin series with Z₀. They are connected to ground at the center point of acapacitor and receive an unbalanced drive. The highlighted portion ofthe Smith chart in FIG. 31( d) depicts the complex impedances that maybe matched by these topologies. FIGS. 31( e),(f),(g) depict threetopologies of matching circuits directly coupled to a high-Q inductiveelement and including inductors in series with Z₀.

FIGS. 32( a),(b),(c) depict three topologies of matching circuitsdirectly coupled to a high-Q inductive element and including capacitorsin series with Z₀. They are connected to ground by tapping at the centerpoint of the inductor loop and receive an unbalanced drive. Thehighlighted portion of the Smith chart in (d) depicts the compleximpedances that may be matched by these topologies, (e),(f),(g) depictthree topologies of matching circuits directly coupled to a high-Qinductive element and including inductors in series with Z₀.

FIGS. 33( a),(b),(c),(d),(e),(f) depict six topologies of matchingcircuits directly coupled to a high-Q inductive element and includingcapacitors in parallel with Z₀. The topologies shown in FIGS. 33(a),(b),(c) are driven with a common-mode signal at the input terminals,while the topologies shown in FIGS. 33( d),(e),(f) are symmetric andreceive a balanced drive. The highlighted portion of the Smith chart inFIG. 33( g) depicts the complex impedances that may be matched by thesetopologies. FIGS. 33( h),(i),(j),(k),(l),(m) depict six topologies ofmatching circuits directly coupled to a high-Q inductive element andincluding inductors in parallel with Z_(o).

FIGS. 34( a),(b),(c) depict three topologies of matching circuitsdirectly coupled to a high-Q inductive element and including capacitorsin parallel with Z₀. They are connected to ground at the center point ofa capacitor and receive an unbalanced drive. The highlighted portion ofthe Smith chart in (d) depicts the complex impedances that may bematched by these topologies. FIGS. 34( e),(f),(g) depict threetopologies of matching circuits directly coupled to a high-Q inductiveelement and including inductors in parallel with Z₀.

FIGS. 35( a),(b),(c) depict three topologies of matching circuitsdirectly coupled to a high-Q inductive element and including capacitorsin parallel with Z₀. They are connected to ground by tapping at thecenter point of the inductor loop and receive an unbalanced drive. Thehighlighted portion of the Smith chart in FIGS. 35( d),(e), and (f)depict the complex impedances that may be matched by these topologies.

FIGS. 36( a),(b),(c),(d) depict four topologies of networks of fixed andvariable capacitors designed to produce an overall variable capacitancewith finer tuning resolution and some with reduced voltage on thevariable capacitor.

FIGS. 37( a) and 37(b) depict two topologies of networks of fixedcapacitors and a variable inductor designed to produce an overallvariable capacitance.

FIG. 38 depicts a high level block diagram of a wireless powertransmission system.

FIG. 39 depicts a block diagram of an exemplary wirelessly powereddevice.

FIG. 40 depicts a block diagram of the source of an exemplary wirelesspower transfer system.

FIG. 41 shows an equivalent circuit diagram of a magnetic resonator. Theslash through the capacitor symbol indicates that the representedcapacitor may be fixed or variable. The port parameter measurementcircuitry may be configured to measure certain electrical signals andmay measure the magnitude and phase of signals.

FIG. 42 shows a circuit diagram of a magnetic resonator where thetunable impedance network is realized with voltage controlledcapacitors. Such an implementation may be adjusted, tuned or controlledby electrical circuits including programmable or controllable voltagesources and/or computer processors. The voltage controlled capacitorsmay be adjusted in response to data measured by the port parametermeasurement circuitry and processed by measurement analysis and controlalgorithms and hardware. The voltage controlled capacitors may be aswitched bank of capacitors.

FIG. 43 shows an end-to-end wireless power transmission system. In thisexample, both the source and the device contain port measurementcircuitry and a processor. The box labeled “coupler/switch” indicatesthat the port measurement circuitry may be connected to the resonator bya directional coupler or a switch, enabling the measurement, adjustmentand control of the source and device resonators to take place inconjunction with, or separate from, the power transfer functionality.

FIG. 44 shows an end-to-end wireless power transmission system. In thisexample, only the source contains port measurement circuitry and aprocessor. In this case, the device resonator operating characteristicsmay be fixed or may be adjusted by analog control circuitry and withoutthe need for control signals generated by a processor.

FIG. 45 shows an end-to-end wireless power transmission system. In thisexample, both the source and the device contain port measurementcircuitry but only the source contains a processor. Data from the deviceis transmitted through a wireless communication channel, which could beimplemented either with a separate antenna, or through some modulationof the source drive signal.

FIG. 46 shows an end-to-end wireless power transmission system. In thisexample, only the source contains port measurement circuitry and aprocessor. Data from the device is transmitted through a wirelesscommunication channel, which could be implemented either with a separateantenna, or through some modulation of the source drive signal.

FIG. 47 shows coupled magnetic resonators whose frequency and impedancemay be automatically adjusted using algorithms implemented using aprocessor or a computer.

FIG. 48 shows a varactor array.

FIG. 49 shows a device (laptop computer) being wirelessly powered orcharged by a source, where both the source and device resonator arephysically separated from, but electrically connected to, the source anddevice.

FIG. 50 (a) is an illustration of a wirelessly powered or charged laptopapplication where the device resonator is inside the laptop case and isnot visible.

FIG. 50 (b) is an illustration of a wirelessly powered or charged laptopapplication where the resonator is underneath the laptop base and iselectrically connected to the laptop power input by an electrical cable.

FIG. 50 (c) is an illustration of a wirelessly powered or charged laptopapplication where the resonator is attached to the laptop base.

FIG. 50 (d) is an illustration of a wirelessly powered or charged laptopapplication where the resonator is attached to the laptop display.

FIG. 51 is a diagram of rooftop PV panels with wireless power transfer.

FIG. 52( a) shows routing of individual traces in four layers of alayered PCB.

FIG. 52( b) is a perspective three dimensional diagram showing routingof individual traces and via connections.

FIG. 53( a) is a diagram showing routing of individual traces in fourlayers of a layered PCB with one of the individual traces highlighted toshow its path through the layer.

FIG. 53( b) is a perspective three dimensional diagram showing routingof conductor traces and via connection with one of the conductor traceshighlighted to show its path through the layers for the stranded trace.

FIGS. 54( a) and 54(b) show examples of alternative routing ofindividual traces.

FIG. 55 is a diagram showing routing of individual traces in one layerof a PCB.

FIG. 56 is a diagram showing routing direction between conducting layersof a PCB.

FIG. 57 is a diagram showing sharing of via space of two stranded tracesrouted next to each other.

FIGS. 58( a)-58(d) are diagrams of cross sections of stranded traceswith various feature sizes and aspect ratios.

DETAILED DESCRIPTION

As described above, this disclosure relates to coupled electromagneticresonators with long-lived oscillatory resonant modes that maywirelessly transfer power from a power supply to a power drain. However,the technique is not restricted to electromagnetic resonators, but isgeneral and may be applied to a wide variety of resonators and resonantobjects. Therefore, we first describe the general technique, and thendisclose electromagnetic examples for wireless energy transfer.

Resonators

A resonator may be defined as a system that can store energy in at leasttwo different forms, and where the stored energy is oscillating betweenthe two forms. The resonance has a specific oscillation mode with aresonant (modal) frequency, f, and a resonant (modal) field. The angularresonant frequency, ω, may be defined as ω=2πf the resonant wavelength,λ, may be defined as λ=c/f, where c is the speed of light, and theresonant period, T, may be defined as T=1/f=2π/ω. In the absence of lossmechanisms, coupling mechanisms or external energy supplying or drainingmechanisms, the total resonator stored energy, W, would stay fixed andthe two forms of energy would oscillate, wherein one would be maximumwhen the other is minimum and vice versa.

In the absence of extraneous materials or objects, the energy in theresonator 102 shown in FIG. 1 may decay or be lost by intrinsic losses.The resonator fields then obey the following linear equation:

${\frac{\mathbb{d}{a(t)}}{\mathbb{d}t} = {{- {{\mathbb{i}}\left( {\omega - {\mathbb{i}\Gamma}} \right)}}{a(t)}}},$where the variable a(t) is the resonant field amplitude, defined so thatthe energy contained within the resonator is given by |a(t)|². Γ is theintrinsic energy decay or loss rate (e.g. due to absorption andradiation losses).

The Quality Factor, or Q-factor, or Q, of the resonator, whichcharacterizes the energy decay, is inversely proportional to theseenergy losses. It may be defined as Q=ω*W/P, where P is thetime-averaged power lost at steady state. That is, a resonator 102 witha high-Q has relatively low intrinsic losses and can store energy for arelatively long time. Since the resonator loses energy at its intrinsicdecay rate, 2Γ, its Q, also referred to as its intrinsic Q, is given byQ=ω/2Γ. The quality factor also represents the number of oscillationperiods, T, it takes for the energy in the resonator to decay by afactor of e.

As described above, we define the quality factor or Q of the resonatoras that due only to intrinsic loss mechanisms. A subscript index such asQ₁, indicates the resonator (resonator 1 in this case) to which the Qrefers. FIG. 2 shows an electromagnetic resonator 102 labeled accordingto this convention. Note that in this figure, there are no extraneousobjects or additional resonators in the vicinity of resonator 1.

Extraneous objects and/or additional resonators in the vicinity of afirst resonator may perturb or load the first resonator, therebyperturbing or loading the Q of the first resonator, depending on avariety of factors such as the distance between the resonator and objector other resonator, the material composition of the object or otherresonator, the structure of the first resonator, the power in the firstresonator, and the like. Unintended external energy losses or couplingmechanisms to extraneous materials and objects in the vicinity of theresonators may be referred to as “perturbing” the Q of a resonator, andmay be indicated by a subscript within rounded parentheses, ( ).Intended external energy losses, associated with energy transfer viacoupling to other resonators and to generators and loads in the wirelessenergy transfer system may be referred to as “loading” the Q of theresonator, and may be indicated by a subscript within square brackets, [].

The Q of a resonator 102 connected or coupled to a power generator, g,or load 302, l, may be called the “loaded quality factor” or the “loadedQ” and may be denoted by Q_(┌g┐) or Q_(┌l┐), as illustrated in FIG. 3.In general, there may be more than one generator or load 302 connectedto a resonator 102. However, we do not list those generators or loadsseparately but rather use “g” and “l” to refer to the equivalent circuitloading imposed by the combinations of generators and loads. In generaldescriptions, we may use the subscript “l” to refer to either generatorsor loads connected to the resonators.

In some of the discussion herein, we define the “loading quality factor”or the “loading Q” due to a power generator or load connected to theresonator, as δQ_([l], where,) 1/δQ_([l])≡1/Q_([l])−1/Q. Note that thelarger the loading Q, δQ_([l]), of a generator or load, the less theloaded Q, Q_([l]), deviates from the unloaded Q of the resonator.

The Q of a resonator in the presence of an extraneous object 402, p,that is not intended to be part of the energy transfer system may becalled the “perturbed quality factor” or the “perturbed Q” and may bedenoted by Q_((p)), as illustrated in FIG. 4. In general, there may bemany extraneous objects, denoted as p1, p2, etc., or a set of extraneousobjects {p}, that perturb the Q of the resonator 102. In this case, theperturbed Q may be denoted Q_((p1+p2+ . . . )) or Q_(({p})). Forexample, Q_(1(brick+wood)) may denote the perturbed quality factor of afirst resonator in a system for wireless power exchange in the presenceof a brick and a piece of wood, and Q_(2({office})) may denote theperturbed quality factor of a second resonator in a system for wirelesspower exchange in an office environment.

In some of the discussion herein, we define the “perturbing qualityfactor” or the “perturbing Q” due to an extraneous object, p, asδQ_((p)), where 1/δQ_((p))≡1/Q_((p))−1/Q. As stated before, theperturbing quality factor may be due to multiple extraneous objects, p1,p2, etc. or a set of extraneous objects, {p}. The larger the perturbingQ, δQ_((p)), of an object, the less the perturbed Q, Q_((p)), deviatesfrom the unperturbed Q of the resonator.

In some of the discussion herein, we also define Θ_((p))≡Q_((p))/Q andcall it the “quality factor insensitivity” or the “Q-insensitivity” ofthe resonator in the presence of an extraneous object. A subscriptindex, such as Θ_(1(p)), indicates the resonator to which the perturbedand unperturbed quality factors are referring, namely,Θ_(1(p))≡Q_(1(p))/Q₁.

Note that the quality factor, Q, may also be characterized as“unperturbed”, when necessary to distinguish it from the perturbedquality factor, Q_((p)), and “unloaded”, when necessary to distinguishit from the loaded quality factor, Q_([l]). Similarly, the perturbedquality factor, Q_((p)), may also be characterized as “unloaded”, whennecessary to distinguish them from the loaded perturbed quality factor,Q_((p)[l]).

Coupled Resonators

Resonators having substantially the same resonant frequency, coupledthrough any portion of their near-fields may interact and exchangeenergy. There are a variety of physical pictures and models that may beemployed to understand, design, optimize and characterize this energyexchange. One way to describe and model the energy exchange between twocoupled resonators is using coupled mode theory (CMT).

In coupled mode theory, the resonator fields obey the following set oflinear equations:

$\frac{\mathbb{d}{a_{m}(t)}}{\mathbb{d}t} = {{{- {{\mathbb{i}}\left( {\omega_{m} - {{\mathbb{i}}\;\Gamma_{m}}} \right)}}{a_{m}(t)}} + {{\mathbb{i}}\;{\sum\limits_{n \neq m}{\kappa_{m\; n}{a_{n}(t)}}}}}$where the indices denote different resonators and κ_(mn) are thecoupling coefficients between the resonators. For a reciprocal system,the coupling coefficients may obey the relation κ_(mn)=κ_(nm). Notethat, for the purposes of the present specification, far-field radiationinterference effects will be ignored and thus the coupling coefficientswill be considered real. Furthermore, since in all subsequentcalculations of system performance in this specification the couplingcoefficients appear only with their square, κ_(mn) ², we use κ_(mn) todenote the absolute value of the real coupling coefficients.

Note that the coupling coefficient, κ_(mn), from the CMT described aboveis related to the so-called coupling factor, k_(mn), between resonatorsm and n by k_(mn)=2κ_(mn)/√{square root over (ω_(m)ω_(n))}. We define a“strong-coupling factor”, U_(mn), as the ratio of the coupling and lossrates between resonators m and n, by U_(mn)=κ_(mn)/√{square root over(Γ_(m)Γ_(n))}=k_(mn)√{square root over (Q_(m)Q_(n))}.

The quality factor of a resonator m, in the presence of a similarfrequency resonator n or additional resonators, may be loaded by thatresonator n or additional resonators, in a fashion similar to theresonator being loaded by a connected power generating or consumingdevice. The fact that resonator m may be loaded by resonator n and viceversa is simply a different way to see that the resonators are coupled.

The loaded Q's of the resonators in these cases may be denoted asQ_(m[n]) and Q_(n[m]). For multiple resonators or loading supplies ordevices, the total loading of a resonator may be determined by modelingeach load as a resistive loss, and adding the multiple loads in theappropriate parallel and/or series combination to determine theequivalent load of the ensemble.

In some of the discussion herein, we define the “loading quality factor”or the “loading Q_(m)” of resonator m due to resonator n as δQ_(m[n]),where 1/δQ_(m[n])≡1/Q_(m[n])−1/Q_(m). Note that resonator n is alsoloaded by resonator m and its “loading Q_(n)” is given by1/δQ_(n[m])≡1/Q_(n[m])−1/Q_(n).

When one or more of the resonators are connected to power generators orloads, the set of linear equations is modified to:

$\frac{\mathbb{d}{a_{m}(t)}}{\mathbb{d}t} = {{{- {{\mathbb{i}}\left( {\omega_{m} - {{\mathbb{i}}\;\Gamma_{m}}} \right)}}{a_{m}(t)}} + {{\mathbb{i}}{\sum\limits_{n \neq m}{\kappa_{m\; n}{a_{n}(t)}}}} - {\kappa_{m}\;{a_{m}(t)}} + {\sqrt{2\kappa_{m}}{s_{+ m}(t)}}}$$\mspace{20mu}{{{s_{- m}(t)} = {{\sqrt{2\kappa_{m}}{a_{m}(t)}} - {s_{+ m}(t)}}},}$where s_(+m)(t) and s_(−m)(t) are respectively the amplitudes of thefields coming from a generator into the resonator m and going out of theresonator m either back towards the generator or into a load, defined sothat the power they carry is given by |s_(+m)(t)|² and s_(−m)(t)|². Theloading coefficients κ_(m) relate to the rate at which energy isexchanged between the resonator m and the generator or load connected toit.

Note that the loading coefficient, κ_(m), from the CMT described aboveis related to the loading quality factor, δQ_(m[l]), defined earlier, byδQ_(m[l])=ω_(m)/2κ_(m).

We define a “strong-loading factor”, U_(m[l]), as the ratio of theloading and loss rates of resonator m,U_(m[l])=κ_(m)/Γ_(m)=Q_(m)/δQ_(m[l].)

FIG. 1( a) shows an example of two coupled resonators 1000, a firstresonator 102S, configured as a source resonator and a second resonator102D, configured as a device resonator. Energy may be transferred over adistance D between the resonators. The source resonator 102S may bedriven by a power supply or generator (not shown). Work may be extractedfrom the device resonator 102D by a power consuming drain or load (e.g.a load resistor, not shown). Let us use the subscripts “s” for thesource, “d” for the device, “g” for the generator, and “1” for the load,and, since in this example there are only two resonators andκ_(sd)=κ_(ds), let us drop the indices on κ_(sd), k_(sd), and U_(sd),and denote them as κ, k, and U, respectively.

The power generator may be constantly driving the source resonator at aconstant driving frequency, f, corresponding to an angular drivingfrequency, ω, where ω=2πf.

In this case, the efficiency, η=|s_(−d)|²/|s_(+s)|², of the powertransmission from the generator to the load (via the source and deviceresonators) is maximized under the following conditions: The sourceresonant frequency, the device resonant frequency and the generatordriving frequency have to be matched, namelyω_(s)ω_(d)=ω.Furthermore, the loading Q of the source resonator due to the generator,δQ_(s[g]), has to be matched (equal) to the loaded Q of the sourceresonator due to the device resonator and the load, Q_(s[dl]), andinversely the loading Q of the device resonator due to the load,δQ_(d[l]), has to be matched (equal) to the loaded Q of the deviceresonator due to the source resonator and the generator, Q_(d[sg]),namelyδQ _(s[g]) =Q _(s[dl]) and δQ _(d[l]) =Q _(d[sg]).These equations determine the optimal loading rates of the sourceresonator by the generator and of the device resonator by the load as

$U_{d{\lbrack l\rbrack}} = {{\kappa_{d}/\Gamma_{d}} = {{{Q_{d}/\delta}\; Q_{d{\lbrack l\rbrack}}} = {\sqrt{1 + U^{2}} = {\sqrt{1 + \left( {\kappa/\sqrt{\Gamma_{s}\Gamma_{d}}} \right)^{2}} = {{{Q_{s}/\delta}\; Q_{s{\lbrack g\rbrack}}} = {{\kappa_{s}/\Gamma_{s}} = {U_{s{\lbrack g\rbrack}}.}}}}}}}$Note that the above frequency matching and Q matching conditions aretogether known as “impedance matching” in electrical engineering.

Under the above conditions, the maximized efficiency is a monotonicallyincreasing function of only the strong-coupling factor, U=κ/√{squareroot over (Γ_(s)Γ_(d))}=k√{square root over (Q_(s)Q_(d))}, between thesource and device resonators and is given by, η=U²/(1+√{square root over(1+U²)})², as shown in FIG. 5. Note that the coupling efficiency, η, isgreater than 1% when U is greater than 0.2, is greater than 10% when Uis greater than 0.7, is greater than 17% when U is greater than 1, isgreater than 52% when U is greater than 3, is greater than 80% when U isgreater than 9, is greater than 90% when U is greater than 19, and isgreater than 95% when U is greater than 45. In some applications, theregime of operation where U>1 may be referred to as the“strong-coupling” regime.

Since a large U=κ/√{square root over (Γ_(s)Γ_(d))}=2κ/√{square root over(ω_(s)ω_(d))})√{square root over (Q_(s)Q_(d))} is desired in certaincircumstances, resonators may be used that are high-Q. The Q of eachresonator may be high. The geometric mean of the resonator Q's, √{squareroot over (Q_(s)Q_(d))} may also or instead be high.

The coupling factor, k, is a number between 0≦k≦1, and it may beindependent (or nearly independent) of the resonant frequencies of thesource and device resonators, rather it may determined mostly by theirrelative geometry and the physical decay-law of the field mediatingtheir coupling. In contrast, the coupling coefficient, κ=k√{square rootover (ω_(s)ω_(d))}/2, may be a strong function of the resonantfrequencies. The resonant frequencies of the resonators may be chosenpreferably to achieve a high Q rather than to achieve a low Γ, as thesetwo goals may be achievable at two separate resonant frequency regimes.

A high-Q resonator may be defined as one with Q>100. Two coupledresonators may be referred to as a system of high-Q resonators when eachresonator has a Q greater than 100, Q_(s)>100 and Q_(d)>100. In otherimplementations, two coupled resonators may be referred to as a systemof high-Q resonators when the geometric mean of the resonator Q's isgreater than 100, √{square root over (Q_(s)Q_(d))}>100.

The resonators may be named or numbered. They may be referred to assource resonators, device resonators, first resonators, secondresonators, repeater resonators, and the like. It is to be understoodthat while two resonators are shown in FIG. 1, and in many of theexamples below, other implementations may include three (3) or moreresonators. For example, a single source resonator 102S may transferenergy to multiple device resonators 102D or multiple devices. Energymay be transferred from a first device to a second, and then from thesecond device to the third, and so forth. Multiple sources may transferenergy to a single device or to multiple devices connected to a singledevice resonator or to multiple devices connected to multiple deviceresonators. Resonators 102 may serve alternately or simultaneously assources, devices, or they may be used to relay power from a source inone location to a device in another location. Intermediateelectromagnetic resonators 102 may be used to extend the distance rangeof wireless energy transfer systems. Multiple resonators 102 may bedaisy chained together, exchanging energy over extended distances andwith a wide range of sources and devices. High power levels may be splitbetween multiple sources 102S, transferred to multiple devices andrecombined at a distant location.

The analysis of a single source and a single device resonator may beextended to multiple source resonators and/or multiple device resonatorsand/or multiple intermediate resonators. In such an analysis, theconclusion may be that large strong-coupling factors, U_(mn), between atleast some or all of the multiple resonators is preferred for a highsystem efficiency in the wireless energy transfer. Again,implementations may use source, device and intermediate resonators thathave a high Q. The Q of each resonator may be high. The geometric mean√{square root over (Q_(m)Q_(n))} of the Q's for pairs of resonators mand n, for which a large U_(mn) is desired, may also or instead be high.

Note that since the strong-coupling factor of two resonators may bedetermined by the relative magnitudes of the loss mechanisms of eachresonator and the coupling mechanism between the two resonators, thestrength of any or all of these mechanisms may be perturbed in thepresence of extraneous objects in the vicinity of the resonators asdescribed above.

Continuing the conventions for labeling from the previous sections, wedescribe k as the coupling factor in the absence of extraneous objectsor materials. We denote the coupling factor in the presence of anextraneous object, p, as k_((p)), and call it the “perturbed couplingfactor” or the “perturbed k”. Note that the coupling factor, k, may alsobe characterized as “unperturbed”, when necessary to distinguish fromthe perturbed coupling factor k_((p)).

We define δk_((p))≡k_((p))−k and we call it the “perturbation on thecoupling factor” or the “perturbation on k” due to an extraneous object,p.

We also define β_((p))≡k_((p))/k and we call it the “coupling factorinsensitivity” or the “k-insensitivity”. Lower indices, such asβ_(12(p)), indicate the resonators to which the perturbed andunperturbed coupling factor is referred to, namelyβ_(12(p))≡k_(12(p))/k₁₂.

Similarly, we describe U as the strong-coupling factor in the absence ofextraneous objects. We denote the strong-coupling factor in the presenceof an extraneous object, p, as U_((p)), U_((p))=k_((p))√{square rootover (Q_(1(p))Q_(2(p)))}{square root over (Q_(1(p))Q_(2(p)))}, and callit the “perturbed strong-coupling factor” or the “perturbed U”. Notethat the strong-coupling factor U may also be characterized as“unperturbed”, when necessary to distinguish from the perturbedstrong-coupling factor U_((p)). Note that the strong-coupling factor Umay also be characterized as “unperturbed”, when necessary todistinguish from the perturbed strong-coupling factor U_((p)).

We define δU_((p))≡U_((p))−U and call it the “perturbation on thestrong-coupling factor” or the “perturbation on U” due to an extraneousobject, p.

We also define Ξ_((p)≡)=U_((p))/U and call it the “strong-couplingfactor insensitivity” or the “U-insensitivity”. Lower indices, such asΞ_(12(p)), indicate the resonators to which the perturbed andunperturbed coupling factor refers, namely Ξ_(12(p))≡U_(12(p))/(U₁₂.

The efficiency of the energy exchange in a perturbed system may be givenby the same formula giving the efficiency of the unperturbed system,where all parameters such as strong-coupling factors, coupling factors,and quality factors are replaced by their perturbed equivalents. Forexample, in a system of wireless energy transfer including one sourceand one device resonator, the optimal efficiency may calculated asη_((p))=[U_((p))/(1+√{square root over (1+U_((p)) ²)})]². Therefore, ina system of wireless energy exchange which is perturbed by extraneousobjects, large perturbed strong-coupling factors, U_(mn(p)), between atleast some or all of the multiple resonators may be desired for a highsystem efficiency in the wireless energy transfer. Source, device and/orintermediate resonators may have a high Q_((p)).

Some extraneous perturbations may sometimes be detrimental for theperturbed strong-coupling factors (via large perturbations on thecoupling factors or the quality factors). Therefore, techniques may beused to reduce the effect of extraneous perturbations on the system andpreserve large strong-coupling factor insensitivites.

Efficiency of Energy Exchange

The so-called “useful” energy in a useful energy exchange is the energyor power that must be delivered to a device (or devices) in order topower or charge the device. The transfer efficiency that corresponds toa useful energy exchange may be system or application dependent. Forexample, high power vehicle charging applications that transferkilowatts of power may need to be at least 80% efficient in order tosupply useful amounts of power resulting in a useful energy exchangesufficient to recharge a vehicle battery, without significantly heatingup various components of the transfer system. In some consumerelectronics applications, a useful energy exchange may include anyenergy transfer efficiencies greater than 10%, or any other amountacceptable to keep rechargeable batteries “topped off” and running forlong periods of time. For some wireless sensor applications, transferefficiencies that are much less than 1% may be adequate for poweringmultiple low power sensors from a single source located a significantdistance from the sensors. For still other applications, where wiredpower transfer is either impossible or impractical, a wide range oftransfer efficiencies may be acceptable for a useful energy exchange andmay be said to supply useful power to devices in those applications. Ingeneral, an operating distance is any distance over which a usefulenergy exchange is or can be maintained according to the principlesdisclosed herein.

A useful energy exchange for a wireless energy transfer in a powering orrecharging application may be efficient, highly efficient, or efficientenough, as long as the wasted energy levels, heat dissipation, andassociated field strengths are within tolerable limits. The tolerablelimits may depend on the application, the environment and the systemlocation. Wireless energy transfer for powering or rechargingapplications may be efficient, highly efficient, or efficient enough, aslong as the desired system performance may be attained for thereasonable cost restrictions, weight restrictions, size restrictions,and the like. Efficient energy transfer may be determined relative tothat which could be achieved using traditional inductive techniques thatare not high-Q systems. Then, the energy transfer may be defined asbeing efficient, highly efficient, or efficient enough, if more energyis delivered than could be delivered by similarly sized coil structuresin traditional inductive schemes over similar distances or alignmentoffsets.

Note that, even though certain frequency and Q matching conditions mayoptimize the system efficiency of energy transfer, these conditions maynot need to be exactly met in order to have efficient enough energytransfer for a useful energy exchange. Efficient energy exchange may berealized so long as the relative offset of the resonant frequencies(|ω_(m)−ω_(n)|/√{square root over (ω_(m)ω_(n))}) is less thanapproximately the maximum among 1/Q_(m(p)), 1/Q_(n(p)) and k_(mn(p)).The Q matching condition may be less critical than the frequencymatching condition for efficient energy exchange. The degree by whichthe strong-loading factors, U_(m[l]), of the resonators due togenerators and/or loads may be away from their optimal values and stillhave efficient enough energy exchange depends on the particular system,whether all or some of the generators and/or loads are Q-mismatched andso on.

Therefore, the resonant frequencies of the resonators may not be exactlymatched, but may be matched within the above tolerances. Thestrong-loading factors of at least some of the resonators due togenerators and/or loads may not be exactly matched to their optimalvalue. The voltage levels, current levels, impedance values, materialparameters, and the like may not be at the exact values described in thedisclosure but will be within some acceptable tolerance of those values.The system optimization may include cost, size, weight, complexity, andthe like, considerations, in addition to efficiency, Q, frequency,strong coupling factor, and the like, considerations. Some systemperformance parameters, specifications, and designs may be far fromoptimal in order to optimize other system performance parameters,specifications and designs.

In some applications, at least some of the system parameters may bevarying in time, for example because components, such as sources ordevices, may be mobile or aging or because the loads may be variable orbecause the perturbations or the environmental conditions are changingetc. In these cases, in order to achieve acceptable matching conditions,at least some of the system parameters may need to be dynamicallyadjustable or tunable. All the system parameters may be dynamicallyadjustable or tunable to achieve approximately the optimal operatingconditions. However, based on the discussion above, efficient enoughenergy exchange may be realized even if some system parameters are notvariable. In some examples, at least some of the devices may not bedynamically adjusted. In some examples, at least some of the sources maynot be dynamically adjusted. In some examples, at least some of theintermediate resonators may not be dynamically adjusted. In someexamples, none of the system parameters may be dynamically adjusted.

Electromagnetic Resonators

The resonators used to exchange energy may be electromagneticresonators. In such resonators, the intrinsic energy decay rates, Γ_(m),are given by the absorption (or resistive) losses and the radiationlosses of the resonator.

The resonator may be constructed such that the energy stored by theelectric field is primarily confined within the structure and that theenergy stored by the magnetic field is primarily in the regionsurrounding the resonator. Then, the energy exchange is mediatedprimarily by the resonant magnetic near-field. These types of resonatorsmay be referred to as magnetic resonators.

The resonator may be constructed such that the energy stored by themagnetic field is primarily confined within the structure and that theenergy stored by the electric field is primarily in the regionsurrounding the resonator. Then, the energy exchange is mediatedprimarily by the resonant electric near-field. These types of resonatorsmay be referred to as electric resonators.

Note that the total electric and magnetic energies stored by theresonator have to be equal, but their localizations may be quitedifferent. In some cases, the ratio of the average electric field energyto the average magnetic field energy specified at a distance from aresonator may be used to characterize or describe the resonator.

Electromagnetic resonators may include an inductive element, adistributed inductance, or a combination of inductances with inductance,L, and a capacitive element, a distributed capacitance, or a combinationof capacitances, with capacitance, C. A minimal circuit model of anelectromagnetic resonator 102 is shown in FIG. 6 a. The resonator mayinclude an inductive element 108 and a capacitive element 104. Providedwith initial energy, such as electric field energy stored in thecapacitor 104, the system will oscillate as the capacitor dischargestransferring energy into magnetic field energy stored in the inductor108 which in turn transfers energy back into electric field energystored in the capacitor 104.

The resonators 102 shown in FIGS. 6( b)(c)(d) may be referred to asmagnetic resonators. Magnetic resonators may be preferred for wirelessenergy transfer applications in populated environments because mosteveryday materials including animals, plants, and humans arenon-magnetic (i.e., μ_(r)≠1), so their interaction with magnetic fieldsis minimal and due primarily to eddy currents induced by thetime-variation of the magnetic fields, which is a second-order effect.This characteristic is important both for safety reasons and because itreduces the potential for interactions with extraneous environmentalobjects and materials that could alter system performance.

FIG. 6 d shows a simplified drawing of some of the electric and magneticfield lines associated with an exemplary magnetic resonator 102B. Themagnetic resonator 102B may include a loop of conductor acting as aninductive element 108 and a capacitive element 104 at the ends of theconductor loop. Note that this drawing depicts most of the energy in theregion surrounding the resonator being stored in the magnetic field, andmost of the energy in the resonator (between the capacitor plates)stored in the electric field. Some electric field, owing to fringingfields, free charges, and the time varying magnetic field, may be storedin the region around the resonator, but the magnetic resonator may bedesigned to confine the electric fields to be close to or within theresonator itself, as much as possible.

The inductor 108 and capacitor 104 of an electromagnetic resonator 102may be bulk circuit elements, or the inductance and capacitance may bedistributed and may result from the way the conductors are formed,shaped, or positioned, in the structure. For example, the inductor 108may be realized by shaping a conductor to enclose a surface area, asshown in FIGS. 6( b)(c)(d). This type of resonator 102 may be referredto as a capacitively-loaded loop inductor. Note that we may use theterms “loop” or “coil” to indicate generally a conducting structure(wire, tube, strip, etc.), enclosing a surface of any shape anddimension, with any number of turns. In FIG. 6 b, the enclosed surfacearea is circular, but the surface may be any of a wide variety of othershapes and sizes and may be designed to achieve certain systemperformance specifications. As an example to indicate how inductancescales with physical dimensions, the inductance for a length of circularconductor arranged to form a circular single-turn loop is approximately,

${L = {\mu_{0}{x\left( {{\ln\;\frac{8x}{a}} - 2} \right)}}},$where μ₀ is the magnetic permeability of free space, x, is the radius ofthe enclosed circular surface area and, a, is the radius of theconductor used to form the inductor loop. A more precise value of theinductance of the loop may be calculated analytically or numerically.

The inductance for other cross-section conductors, arranged to formother enclosed surface shapes, areas, sizes, and the like, and of anynumber of wire turns, may be calculated analytically, numerically or itmay be determined by measurement. The inductance may be realized usinginductor elements, distributed inductance, networks, arrays, series andparallel combinations of inductors and inductances, and the like. Theinductance may be fixed or variable and may be used to vary impedancematching as well as resonant frequency operating conditions.

There are a variety of ways to realize the capacitance required toachieve the desired resonant frequency for a resonator structure.Capacitor plates 110 may be formed and utilized as shown in FIG. 6 b, orthe capacitance may be distributed and be realized between adjacentwindings of a multi-loop conductor 114, as shown in FIG. 6 c. Thecapacitance may be realized using capacitor elements, distributedcapacitance, networks, arrays, series and parallel combinations ofcapacitances, and the like. The capacitance may be fixed or variable andmay be used to vary impedance matching as well as resonant frequencyoperating conditions.

It is to be understood that the inductance and capacitance in anelectromagnetic resonator 102 may be lumped, distributed, or acombination of lumped and distributed inductance and capacitance andthat electromagnetic resonators may be realized by combinations of thevarious elements, techniques and effects described herein.

Electromagnetic resonators 102 may be include inductors, inductances,capacitors, capacitances, as well as additional circuit elements such asresistors, diodes, switches, amplifiers, diodes, transistors,transformers, conductors, connectors and the like.

Resonant Frequency of an Electromagnetic Resonator

An electromagnetic resonator 102 may have a characteristic, natural, orresonant frequency determined by its physical properties. This resonantfrequency is the frequency at which the energy stored by the resonatoroscillates between that stored by the electric field, W_(E),(W_(E)=q²/2C, where q is the charge on the capacitor, C) and that storedby the magnetic field, W_(B), (W_(B)=Li²/2, where i is the currentthrough the inductor, L) of the resonator. In the absence of any lossesin the system, energy would continually be exchanged between theelectric field in the capacitor 104 and the magnetic field in theinductor 108. The frequency at which this energy is exchanged may becalled the characteristic frequency, the natural frequency, or theresonant frequency of the resonator, and is given by ω,

$\omega = {{2\pi\; f} = {\sqrt{\frac{1}{LC}}.}}$

The resonant frequency of the resonator may be changed by tuning theinductance, L, and/or the capacitance, C, of the resonator. Theresonator frequency may be design to operate at the so-called ISM(Industrial, Scientific and Medical) frequencies as specified by theFCC. The resonator frequency may be chosen to meet certain field limitspecifications, specific absorption rate (SAR) limit specifications,electromagnetic compatibility (EMC) specifications, electromagneticinterference (EMI) specifications, component size, cost or performancespecifications, and the like.

Quality Factor of an Electromagnetic Resonator

The energy in the resonators 102 shown in FIG. 6 may decay or be lost byintrinsic losses including absorptive losses (also called ohmic orresistive losses) and/or radiative losses. The Quality Factor, or Q, ofthe resonator, which characterizes the energy decay, is inverselyproportional to these losses. Absorptive losses may be caused by thefinite conductivity of the conductor used to form the inductor as wellas by losses in other elements, components, connectors, and the like, inthe resonator. An inductor formed from low loss materials may bereferred to as a “high-Q inductive element” and elements, components,connectors and the like with low losses may be referred to as having“high resistive Q's”. In general, the total absorptive loss for aresonator may be calculated as the appropriate series and/or parallelcombination of resistive losses for the various elements and componentsthat make up the resonator. That is, in the absence of any significantradiative or component/connection losses, the Q of the resonator may begiven by, Q_(abs),

${Q_{{ab}\; s} = \frac{\omega\; L}{R_{a\;{bs}}}},$where ω, is the resonant frequency, L, is the total inductance of theresonator and the resistance for the conductor used to form theinductor, for example, may be given by R_(abs)=lρ/A,(l is the length ofthe wire, ρ is the resistivity of the conductor material, and A is thecross-sectional area over which current flows in the wire). Foralternating currents, the cross-sectional area over which current flowsmay be less than the physical cross-sectional area of the conductorowing to the skin effect. Therefore, high-Q magnetic resonators may becomposed of conductors with high conductivity, relatively large surfaceareas and/or with specially designed profiles (e.g. Litz wire) tominimize proximity effects and reduce the AC resistance.

The magnetic resonator structures may include high-Q inductive elementscomposed of high conductivity wire, coated wire, Litz wire, ribbon,strapping or plates, tubing, paint, gels, traces, and the like. Themagnetic resonators may be self-resonant, or they may include externalcoupled elements such as capacitors, inductors, switches, diodes,transistors, transformers, and the like. The magnetic resonators mayinclude distributed and lumped capacitance and inductance. In general,the Q of the resonators will be determined by the Q's of all theindividual components of the resonator.

Because Q is proportional to inductance, L, resonators may be designedto increase L, within certain other constraints. One way to increase L,for example, is to use more than one turn of the conductor to form theinductor in the resonator. Design techniques and trade-offs may dependon the application, and a wide variety of structures, conductors,components, and resonant frequencies may be chosen in the design ofhigh-Q magnetic resonators.

In the absence of significant absorption losses, the Q of the resonatormay be determined primarily by the radiation losses, and given by,Q_(rad)=ωL/R_(rad), where R_(rad) is the radiative loss of the resonatorand may depend on the size of the resonator relative to the frequency,ω, or wavelength, λ, of operation. For the magnetic resonators discussedabove, radiative losses may scale as R_(rad)˜(x/λ)⁴ (characteristic ofmagnetic dipole radiation), where x is a characteristic dimension of theresonator, such as the radius of the inductive element shown in FIG. 6b, and where λ=c/f, where c is the speed of light and f is as definedabove. The size of the magnetic resonator may be much less than thewavelength of operation so radiation losses may be very small. Suchstructures may be referred to as sub-wavelength resonators. Radiationmay be a loss mechanism for non-radiative wireless energy transfersystems and designs may be chosen to reduce or minimize R_(rad). Notethat a high-Q_(rad) may be desirable for non-radiative wireless energytransfer schemes.

Note too that the design of resonators for non-radiative wireless energytransfer differs from antennas designed for communication or far-fieldenergy transmission purposes. Specifically, capacitively-loadedconductive loops may be used as resonant antennas (for example in cellphones), but those operate in the far-field regime where the radiationQ's are intentionally designed to be small to make the antenna efficientat radiating energy. Such designs are not appropriate for the efficientnear-field wireless energy transfer technique disclosed in thisapplication.

The quality factor of a resonator including both radiative andabsorption losses is Q=ωL/(R_(abs)+R_(rad)). Note that there may be amaximum Q value for a particular resonator and that resonators may bedesigned with special consideration given to the size of the resonator,the materials and elements used to construct the resonator, theoperating frequency, the connection mechanisms, and the like, in orderto achieve a high-Q resonator. FIG. 7 shows a plot of Q of an exemplarymagnetic resonator (in this case a coil with a diameter of 60 cm made ofcopper pipe with an outside diameter (OD) of 4 cm) that may be used forwireless power transmission at MHz frequencies. The absorptive Q (dashedline) 702 increases with frequency, while the radiative Q (dotted line)704 decreases with frequency, thus leading the overall Q to peak 708 ata particular frequency. Note that the Q of this exemplary resonator isgreater than 100 over a wide frequency range. Magnetic resonators may bedesigned to have high-Q over a range of frequencies and system operatingfrequency may set to any frequency in that range.

When the resonator is being described in terms of loss rates, the Q maybe defined using the intrinsic decay rate, 2Γ, as described previously.The intrinsic decay rate is the rate at which an uncoupled and undrivenresonator loses energy. For the magnetic resonators described above, theintrinsic loss rate may be given by Γ=(R_(abs)+R_(rad))/2L, and thequality factor, Q, of the resonator is given by Q=ω/2Γ

Note that a quality factor related only to a specific loss mechanism maybe denoted as Q_(mechanism), if the resonator is not specified, or asQ_(1,mechanism), if the resonator is mechanism, specified (e.g.resonator 1). For example, Q_(1,rad) is the quality factor for resonator1 related to its radiation losses.

Electromagnetic Resonator Near-Fields

The high-Q electromagnetic resonators used in the near-field wirelessenergy transfer system disclosed here may be sub-wavelength objects.That is, the physical dimensions of the resonator may be much smallerthan the wavelength corresponding to the resonant frequency.Sub-wavelength magnetic resonators may have most of the energy in theregion surrounding the resonator stored in their magnetic near-fields,and these fields may also be described as stationary or non-propagatingbecause they do not radiate away from the resonator. The extent of thenear-field in the area surrounding the resonator is typically set by thewavelength, so it may extend well beyond the resonator itself for asub-wavelength resonator. The limiting surface, where the field behaviorchanges from near-field behavior to far-field behavior may be called the“radiation caustic”.

The strength of the near-field is reduced the farther one gets away fromthe resonator. While the field strength of the resonator near-fieldsdecays away from the resonator, the fields may still interact withobjects brought into the general vicinity of the resonator. The degreeto which the fields interact depends on a variety of factors, some ofwhich may be controlled and designed, and some of which may not. Thewireless energy transfer schemes described herein may be realized whenthe distance between coupled resonators is such that one resonator lieswithin the radiation caustic of the other.

The near-field profiles of the electromagnetic resonators may be similarto those commonly associated with dipole resonators or oscillators. Suchfield profiles may be described as omni-directional, meaning themagnitudes of the fields are non-zero in all directions away from theobject.

Characteristic Size of an Electromagnetic Resonator

Spatially separated and/or offset magnetic resonators of sufficient Qmay achieve efficient wireless energy transfer over distances that aremuch larger than have been seen in the prior art, even if the sizes andshapes of the resonator structures are different. Such resonators mayalso be operated to achieve more efficient energy transfer than wasachievable with previous techniques over shorter range distances. Wedescribe such resonators as being capable of mid-range energy transfer.

Mid-range distances may be defined as distances that are larger than thecharacteristic dimension of the smallest of the resonators involved inthe transfer, where the distance is measured from the center of oneresonator structure to the center of a spatially separated secondresonator structure. In this definition, two-dimensional resonators arespatially separated when the areas circumscribed by their inductiveelements do not intersect and three-dimensional resonators are spatiallyseparated when their volumes do not intersect. A two-dimensionalresonator is spatially separated from a three-dimensional resonator whenthe area circumscribed by the former is outside the volume of thelatter.

FIG. 8 shows some example resonators with their characteristicdimensions labeled. It is to be understood that the characteristic sizes802 of resonators 102 may be defined in terms of the size of theconductor and the area circumscribed or enclosed by the inductiveelement in a magnetic resonator and the length of the conductor formingthe capacitive element of an electric resonator. Then, thecharacteristic size 802 of a resonator 102, x_(char), may be equal tothe radius of the smallest sphere that can fit around the inductive orcapacitive element of the magnetic or electric resonator respectively,and the center of the resonator structure is the center of the sphere.The characteristic thickness 804, t_(char), of a resonator 102 may bethe smallest possible height of the highest point of the inductive orcapacitive element in the magnetic or capacitive resonator respectively,measured from a flat surface on which it is placed. The characteristicwidth 808 of a resonator 102, w_(char), may be the radius of thesmallest possible circle through which the inductive or capacitiveelement of the magnetic or electric resonator respectively, may passwhile traveling in a straight line. For example, the characteristicwidth 808 of a cylindrical resonator may be the radius of the cylinder.

In this inventive wireless energy transfer technique, energy may beexchanged efficiently over a wide range of distances, but the techniqueis distinguished by the ability to exchange useful energy for poweringor recharging devices over mid-range distances and between resonatorswith different physical dimensions, components and orientations. Notethat while k may be small in these circumstances, strong coupling andefficient energy transfer may be realized by using high-Q resonators toachieve a high U, U=k√{square root over (Q_(s)Q_(d))}. That is,increases in Q may be used to at least partially overcome decreases ink, to maintain useful energy transfer efficiencies.

Note too that while the near-field of a single resonator may bedescribed as omni-directional, the efficiency of the energy exchangebetween two resonators may depend on the relative position andorientation of the resonators. That is, the efficiency of the energyexchange may be maximized for particular relative orientations of theresonators. The sensitivity of the transfer efficiency to the relativeposition and orientation of two uncompensated resonators may be capturedin the calculation of either k or κ. While coupling may be achievedbetween resonators that are offset and/or rotated relative to eachother, the efficiency of the exchange may depend on the details of thepositioning and on any feedback, tuning, and compensation techniquesimplemented during operation.

High-Q Magnetic Resonators

In the near-field regime of a sub-wavelength capacitively-loaded loopmagnetic resonator (x<<λ), the resistances associated with a circularconducting loop inductor composed of N turns of wire whose radius islarger than the skin depth, are approximately R_(abs)=√{square root over(μ_(o)ρω/2)}·Nx/α and R_(rad)=π/6·η_(o)N²(ωx/c)⁴, where ρ is theresistivity of the conductor material and η_(o)≈120π Ω is the impedanceof free space. The inductance, L, for such a N-turn loop isapproximately N² times the inductance of a single-turn loop givenpreviously. The quality factor of such a resonator,Q=ωL/(R_(abs)+R_(rad)), is highest for a particular frequency determinedby the system parameters (FIG. 4). As described previously, at lowerfrequencies the Q is determined primarily by absorption losses and athigher frequencies the Q is determined primarily by radiation losses.

Note that the formulas given above are approximate and intended toillustrate the functional dependence of R_(abs), R_(rad) and L on thephysical parameters of the structure. More accurate numericalcalculations of these parameters that take into account deviations fromthe strict quasi-static limit, for example a non-uniform current/chargedistribution along the conductor, may be useful for the precise designof a resonator structure.

Note that the absorptive losses may be minimized by using low lossconductors to form the inductive elements. The loss of the conductorsmay be minimized by using large surface area conductors such asconductive tubing, strapping, strips, machined objects, plates, and thelike, by using specially designed conductors such as Litz wire, braidedwires, wires of any cross-section, and other conductors with lowproximity losses, in which case the frequency scaled behavior describedabove may be different, and by using low resistivity materials such ashigh-purity copper and silver, for example. One advantage of usingconductive tubing as the conductor at higher operating frequencies isthat it may be cheaper and lighter than a similar diameter solidconductor, and may have similar resistance because most of the currentis traveling along the outer surface of the conductor owing to the skineffect.

To get a rough estimate of achievable resonator designs made from copperwire or copper tubing and appropriate for operation in the microwaveregime, one may calculate the optimum Q and resonant frequency for aresonator composed of one circular inductive element (N=1) of copperwire (ρ=1.69·10⁻⁸ Ωm) with various cross sections. Then for an inductiveelement with characteristic size x=1 cm and conductor diameter a=1 mm,appropriate for a cell phone for example, the quality factor peaks atQ=1225 when f=380 MHz. For x=30 cm and a=2 mm, an inductive element sizethat might be appropriate for a laptop or a household robot, Q=1103 atf=17 MHz. For a larger source inductive element that might be located inthe ceiling for example, x=1 m and a=4 mm, Q may be as high as Q=1315 atf=5 MHz. Note that a number of practical examples yield expected qualityfactors of Q≈1000-1500 at λ/x≈50-80. Measurements of a wider variety ofcoil shapes, sizes, materials and operating frequencies than describedabove show that Q's>100 may be realized for a variety of magneticresonator structures using commonly available materials.

As described above, the rate for energy transfer between two resonatorsof characteristic size x₁ and x₂, and separated by a distance D betweentheir centers, may be given by κ. To give an example of how the definedparameters scale, consider the cell phone, laptop, and ceiling resonatorexamples from above, at three (3) distances; D/x=10, 8, 6. In theexamples considered here, the source and device resonators are the samesize, x₁=x₂, and shape, and are oriented as shown in FIG. 1( b). In thecell phone example, ω/2κ=3033, 1553, 655 respectively. In the laptopexample, ω/2κ=7131, 3651, 1540 respectively and for the ceilingresonator example, ω/2κ=6481, 3318, 1400. The correspondingcoupling-to-loss ratios peak at the frequency where the inductiveelement Q peaks and are κ/Γ=0.4, 0.79, 1.97 and 0.15, 0.3, 0.72 and 0.2,0.4, 0.94 for the three inductive element sizes and distances describedabove. An example using different sized inductive elements is that of anx₁=1 m inductor (e.g. source in the ceiling) and an x₂=30 cm inductor(e.g. household robot on the floor) at a distance D=3 m apart (e.g. roomheight). In this example, the strong-coupling figure of merit,U=κ/√{square root over (Γ₁Γ₂)}=0.88, for an efficiency of approximately14%, at the optimal operating frequency of f=6.4 MHz. Here, the optimalsystem operating frequency lies between the peaks of the individualresonator Q's.

Inductive elements may be formed for use in high-Q magnetic resonators.We have demonstrated a variety of high-Q magnetic resonators based oncopper conductors that are formed into inductive elements that enclose asurface. Inductive elements may be formed using a variety of conductorsarranged in a variety of shapes, enclosing any size or shaped area, andthey may be single turn or multiple turn elements. Drawings of exemplaryinductive elements 900A-B are shown in FIG. 9. The inductive elementsmay be formed to enclose a circle, a rectangle, a square, a triangle, ashape with rounded corners, a shape that follows the contour of aparticular structure or device, a shape that follows, fills, orutilizes, a dedicated space within a structure or device, and the like.The designs may be optimized for size, cost, weight, appearance,performance, and the like.

These conductors may be bent or formed into the desired size, shape, andnumber of turns. However, it may be difficult to accurately reproduceconductor shapes and sizes using manual techniques. In addition, it maybe difficult to maintain uniform or desired center-to-center spacingsbetween the conductor segments in adjacent turns of the inductiveelements. Accurate or uniform spacing may be important in determiningthe self capacitance of the structure as well as any proximity effectinduced increases in AC resistance, for example.

Molds may be used to replicate inductor elements for high-Q resonatordesigns. In addition, molds may be used to accurately shape conductorsinto any kind of shape without creating kinks, buckles or otherpotentially deleterious effects in the conductor. Molds may be used toform the inductor elements and then the inductor elements may be removedfrom the forms. Once removed, these inductive elements may be built intoenclosures or devices that may house the high-Q magnetic resonator. Theformed elements may also or instead remain in the mold used to formthem.

The molds may be formed using standard CNC (computer numerical control)routing or milling tools or any other known techniques for cutting orforming grooves in blocks. The molds may also or instead be formed usingmachining techniques, injection molding techniques, casting techniques,pouring techniques, vacuum techniques, thermoforming techniques,cut-in-place techniques, compression forming techniques and the like.

The formed element may be removed from the mold or it may remain in themold. The mold may be altered with the inductive element inside. Themold may be covered, machined, attached, painted and the like. The moldand conductor combination may be integrated into another housing,structure or device. The grooves cut into the molds may be any dimensionand may be designed to form conducting tubing, wire, strapping, strips,blocks, and the like into the desired inductor shapes and sizes.

The inductive elements used in magnetic resonators may contain more thanone loop and may spiral inward or outward or up or down or in somecombination of directions. In general, the magnetic resonators may havea variety of shapes, sizes and number of turns and they may be composedof a variety of conducing materials.

The magnetic resonators may be free standing or they may be enclosed inan enclosure, container, sleeve or housing. The magnetic resonators mayinclude the form used to make the inductive element. These various formsand enclosures may be composed of almost any kind of material. Low lossmaterials such as Teflon, REXOLITE, styrene, and the like may bepreferable for some applications. These enclosures may contain fixturesthat hold the inductive elements.

Magnetic resonators may be composed of self-resonant coils of copperwire or copper tubing. Magnetic resonators composed of self resonantconductive wire coils may include a wire of length l, and cross sectionradius a, wound into a helical coil of radius x, height h, and number ofturns N, which may for example be characterized as N=√{square root over(l²−h²)}/2πx.

A magnetic resonator structure may be configured so that x is about 30cm, h is about 20 cm, a is about 3 mm and N is about 5.25, and, duringoperation, a power source coupled to the magnetic resonator may drivethe resonator at a resonant frequency, f, where f is about 10.6 MHz.Where x is about 30 cm, h is about 20 cm, a is about 1 cm and N is about4, the resonator may be driven at a frequency, f, where f is about 13.4MHz. Where x is about 10 cm, h is about 3 cm, a is about 2 mm and N isabout 6, the resonator may be driven at a frequency, f, where f is about21.4 MHz.

High-Q inductive elements may be designed using printed circuit boardtraces. Printed circuit board traces may have a variety of advantagescompared to mechanically formed inductive elements including that theymay be accurately reproduced and easily integrated using establishedprinted circuit board fabrication techniques, that their AC resistancemay be lowered using custom designed conductor traces, and that the costof mass-producing them may be significantly reduced.

High-Q inductive elements may be fabricated using standard PCBtechniques on any PCB material such as FR-4 (epoxy E-glass),multi-functional epoxy, high performance epoxy, bismalaimidetriazine/epoxy, polyimide, Cyanate Ester, polytetraflouroethylene(Teflon), FR-2, FR-3, CEM-1, CEM-2, Rogers, Resolute, and the like. Theconductor traces may be formed on printed circuit board materials withlower loss tangents.

The conducting traces may be composed of copper, silver, gold, aluminum,nickel and the like, and they may be composed of paints, inks, or othercured materials. The circuit board may be flexible and it may be aflex-circuit. The conducting traces may be formed by chemicaldeposition, etching, lithography, spray deposition, cutting, and thelike. The conducting traces may be applied to form the desired patternsand they may be formed using crystal and structure growth techniques.

The dimensions of the conducting traces, as well as the number of layerscontaining conducting traces, the position, size and shape of thosetraces and the architecture for interconnecting them may be designed toachieve or optimize certain system specifications such as resonator Q,Q_((p)), resonator size, resonator material and fabrication costs, U,U_((p)), and the like.

As an example, a three-turn high-Q inductive element 1001A wasfabricated on a four-layer printed circuit board using the rectangularcopper trace pattern as shown in FIG. 10( a). The copper trace is shownin black and the PCB in white. The width and thickness of the coppertraces in this example was approximately 1 cm (400 mils) and 43 μm (1.7mils) respectively. The edge-to-edge spacing between turns of theconducting trace on a single layer was approximately 0.75 cm (300 mils)and each board layer thickness was approximately 100 μm (4 mils). Thepattern shown in FIG. 10( a) was repeated on each layer of the board andthe conductors were connected in parallel. The outer dimensions of the3-loop structure were approximately 30 cm by 20 cm. The measuredinductance of this PCB loop was 5.3μ H. A magnetic resonator using thisinductor element and tunable capacitors had a quality factor, Q, of 550at its designed resonance frequency of 6.78 MHz. The resonant frequencycould be tuned by changing the inductance and capacitance values in themagnetic resonator.

As another example, a two-turn inductor 1001B was fabricated on afour-layer printed circuit board using the rectangular copper tracepattern shown in FIG. 10( b). The copper trace is shown in black and thePCB in white. The width and height of the copper traces in this examplewere approximately 0.75 cm (300 mils) and 43 μm (1.7 mils) respectively.The edge-to-edge spacing between turns of the conducting trace on asingle layer was approximately 0.635 cm (250 mils) and each board layerthickness was approximately 100 μm (4 mils). The pattern shown in FIG.10( b) was repeated on each layer of the board and the conductors wereconnected in parallel. The outer dimensions of the two-loop structurewere approximately 7.62 cm by 26.7 cm. The measured inductance of thisPCB loop was 1.3 μH. Stacking two boards together with a verticalseparation of approximately 0.635 cm (250 mils) and connecting the twoboards in series produced a PCB inductor with an inductance ofapproximately 3.4 μH. A magnetic resonator using this stacked inductorloop and tunable capacitors had a quality factor, Q, of 390 at itsdesigned resonance frequency of 6.78 MHz. The resonant frequency couldbe tuned by changing the inductance and capacitance values in themagnetic resonator.

The inductive elements may be formed using magnetic materials of anysize, shape thickness, and the like, and of materials with a wide rangeof permeability and loss values. These magnetic materials may be solidblocks, they may enclose hollow volumes, they may be formed from manysmaller pieces of magnetic material tiled and or stacked together, andthey may be integrated with conducting sheets or enclosures made fromhighly conducting materials. Wires may be wrapped around the magneticmaterials to generate the magnetic near-field. These wires may bewrapped around one or more than one axis of the structure. Multiplewires may be wrapped around the magnetic materials and combined inparallel, or in series, or via a switch to form customized near-fieldpatterns.

The magnetic resonator may include 15 turns of Litz wire wound around a19.2 cm×10 cm×5 mm tiled block of 3F3 ferrite material. The Litz wiremay be wound around the ferrite material in any direction or combinationof directions to achieve the desire resonator performance. The number ofturns of wire, the spacing between the turns, the type of wire, the sizeand shape of the magnetic materials and the type of magnetic materialare all design parameters that may be varied or optimized for differentapplication scenarios.

High-Q Magnetic Resonators Using Magnetic Material Structures

It may be possible to use magnetic materials assembled to form an openmagnetic circuit, albeit one with an air gap on the order of the size ofthe whole structure, to realize a magnetic resonator structure. In thesestructures, high conductivity materials are wound around a structuremade from magnetic material to form the inductive element of themagnetic resonator. Capacitive elements may be connected to the highconductivity materials, with the resonant frequency then determined asdescribed above. These magnetic resonators have their dipole moment inthe plane of the two dimensional resonator structures, rather thanperpendicular to it, as is the case for the capacitively-loaded inductorloop resonators.

A diagram of a single planar resonator structure is shown in FIG. 11(a). The planar resonator structure is constructed of a core of magneticmaterial 1121, such as ferrite with a loop or loops of conductingmaterial 1122 wrapped around the core 1121. The structure may be used asthe source resonator that transfers power and the device resonator thatcaptures energy. When used as a source, the ends of the conductor may becoupled to a power source. Alternating electrical current flowingthrough the conductor loops excites alternating magnetic fields. Whenthe structure is being used to receive power, the ends of the conductormay be coupled to a power drain or load. Changing magnetic fields inducean electromotive force in the loop or loops of the conductor woundaround the core magnetic material. The dipole moment of these types ofstructures is in the plane of the structures and is, for example,directed along the Y axis for the structure in FIG. 11( a). Two suchstructures have strong coupling when placed substantially in the sameplane (i.e. the X,Y plane of FIG. 11). The structures of FIG. 11( a)have the most favorable orientation when the resonators are aligned inthe same plane along their Y axis.

The geometry and the coupling orientations of the described planarresonators may be preferable for some applications. The planar or flatresonator shape may be easier to integrate into many electronic devicesthat are relatively flat and planar. The planar resonators may beintegrated into the whole back or side of a device without requiring achange in geometry of the device. Due to the flat shape of many devices,the natural position of the devices when placed on a surface is to laywith their largest dimension being parallel to the surface they areplaced on. A planar resonator integrated into a flat device is naturallyparallel to the plane of the surface and is in a favorable couplingorientation relative to the resonators of other devices or planarresonator sources placed on a flat surface.

As mentioned, the geometry of the planar resonators may allow easierintegration into devices. Their low profile may allow a resonator to beintegrated into or as part of a complete side of a device. When a wholeside of a device is covered by the resonator, magnetic flux can flowthrough the resonator core without being obstructed by lossy materialthat may be part of the device or device circuitry.

The core of the planar resonator structure may be of a variety of shapesand thicknesses and may be flat or planar such that the minimumdimension does not exceed 30% of the largest dimension of the structure.The core may have complex geometries and may have indentations, notches,ridges, and the like. Geometric enhancements may be used to reduce thecoupling dependence on orientation and they may be used to facilitateintegration into devices, packaging, packages, enclosures, covers,skins, and the like. Two exemplary variations of core geometries areshown in FIG. 11( b). For example, the planar core 1131 may be shapedsuch that the ends are substantially wider than the middle of thestructure to create an indentation for the conductor winding. The corematerial may be of varying thickness with ends that are thicker andwider than the middle. The core material 1132 may have any number ofnotches or cutouts 1133 of various depths, width, and shapes toaccommodate conductor loops, housing, packaging, and the like.

The shape and dimensions of the core may be further dictated by thedimensions and characteristics of the device that they are integratedinto. The core material may curve to follow the contours of the device,or may require non-symmetric notches or cutouts to allow clearance forparts of the device. The core structure may be a single monolithic pieceof magnetic material or may be composed of a plurality of tiles, blocks,or pieces that are arranged together to form the larger structure. Thedifferent layers, tiles, blocks, or pieces of the structure may be ofsimilar or may be of different materials. It may be desirable to usematerials with different magnetic permeability in different locations ofthe structure. Core structures with different magnetic permeability maybe useful for guiding the magnetic flux, improving coupling, andaffecting the shape or extent of the active area of a system.

The conductor of the planar resonator structure may be wound at leastonce around the core. In certain circumstances, it may be preferred towind at least three loops. The conductor can be any good conductorincluding conducting wire, Litz wire, conducting tubing, sheets, strips,gels, inks, traces and the like.

The size, shape, or dimensions of the active area of source may befurther enhanced, altered, or modified with the use of materials thatblock, shield, or guide magnetic fields. To create non-symmetric activearea around a source once side of the source may be covered with amagnetic shield to reduce the strength of the magnetic fields in aspecific direction. The shield may be a conductor or a layeredcombination of conductor and magnetic material which can be used toguide magnetic fields away from a specific direction. Structurescomposed of layers of conductors and magnetic materials may be used toreduce energy losses that may occur due to shielding of the source.

The plurality of planar resonators may be integrated or combined intoone planar resonator structure. A conductor or conductors may be woundaround a core structure such that the loops formed by the two conductorsare not coaxial. An example of such a structure is shown in FIG. 12where two conductors 1201,1202 are wrapped around a planar rectangularcore 1203 at orthogonal angles. The core may be rectangular or it mayhave various geometries with several extensions or protrusions. Theprotrusions may be useful for wrapping of a conductor, reducing theweight, size, or mass of the core, or may be used to enhance thedirectionality or omni-directionality of the resonator. A multi wrappedplanar resonator with four protrusions is shown by the inner structure1310 in FIG. 13, where four conductors 1301, 1302, 1303, 1304 arewrapped around the core. The core may have extensions1305,1306,1307,1308 with one or more conductor loops. A single conductormay be wrapped around a core to form loops that are not coaxial. Thefour conductor loops of FIG. 13, for example, may be formed with onecontinuous piece of conductor, or using two conductors where a singleconductor is used to make all coaxial loops.

Non-uniform or asymmetric field profiles around the resonator comprisinga plurality of conductor loops may be generated by driving someconductor loops with non-identical parameters. Some conductor loops of asource resonator with a plurality of conductor loops may be driven by apower source with a different frequency, voltage, power level, dutycycle, and the like all of which may be used to affect the strength ofthe magnetic field generated by each conductor.

The planar resonator structures may be combined with acapacitively-loaded inductor resonator coil to provide anomni-directional active area all around, including above and below thesource while maintaining a flat resonator structure. As shown in FIG.13, an additional resonator loop coil 1309 comprising of a loop or loopsof a conductor, may be placed in a common plane as the planar resonatorstructure 1310. The outer resonator coil provides an active area that issubstantially above and below the source. The resonator coil can bearranged with any number of planar resonator structures and arrangementsdescribed herein.

The planar resonator structures may be enclosed in magneticallypermeable packaging or integrated into other devices. The planar profileof the resonators within a single, common plane allows packaging andintegration into flat devices. A diagram illustrating the application ofthe resonators is shown in FIG. 14. A flat source 1411 comprising one ormore planar resonators 1414 each with one or more conductor loops maytransfer power to devices 1412,1413 that are integrated with otherplanar resonators 1415,1416 and placed within an active area 1417 of thesource. The devices may comprise a plurality of planar resonators suchthat regardless of the orientation of the device with respect to thesource the active area of the source does not change. In addition toinvariance to rotational misalignment, a flat device comprising ofplanar resonators may be turned upside down without substantiallyaffecting the active area since the planar resonator is still in theplane of the source.

Another diagram illustrating a possible use of a power transfer systemusing the planar resonator structures is shown in FIG. 15. A planarsource 1521 placed on top of a surface 1525 may create an active areathat covers a substantial surface area creating an “energized surface”area. Devices such as computers 1524, mobile handsets 1522, games, andother electronics 1523 that are coupled to their respective planardevice resonators may receive energy from the source when placed withinthe active area of the source, which may be anywhere on top of thesurface. Several devices with different dimensions may be placed in theactive area and used normally while charging or being powered from thesource without having strict placement or alignment constraints. Thesource may be placed under the surface of a table, countertop, desk,cabinet, and the like, allowing it to be completely hidden whileenergizing the top surface of the table, countertop, desk, cabinet andthe like, creating an active area on the surface that is much largerthan the source.

The source may include a display or other visual, auditory, or vibrationindicators to show the direction of charging devices or what devices arebeing charged, error or problems with charging, power levels, chargingtime, and the like.

The source resonators and circuitry may be integrated into any number ofother devices. The source may be integrated into devices such as clocks,keyboards, monitors, picture frames, and the like. For example, akeyboard integrated with the planar resonators and appropriate power andcontrol circuitry may be used as a source for devices placed around thekeyboard such as computer mice, webcams, mobile handsets, and the likewithout occupying any additional desk space.

While the planar resonator structures have been described in the contextof mobile devices it should be clear to those skilled in the art that aflat planar source for wireless power transfer with an active area thatextends beyond its physical dimensions has many other consumer andindustrial applications. The structures and configuration may be usefulfor a large number of applications where electronic or electric devicesand a power source are typically located, positioned, or manipulated insubstantially the same plane and alignment. Some of the possibleapplication scenarios include devices on walls, floor, ceilings or anyother substantially planar surfaces.

Flat source resonators may be integrated into a picture frame or hung ona wall thereby providing an active area within the plane of the wallwhere other electronic devices such as digital picture frames,televisions, lights, and the like can be mounted and powered withoutwires. Planar resonators may be integrated into a floor resulting in anenergized floor or active area on the floor on which devices can beplaced to receive power. Audio speakers, lamps, heaters, and the likecan be placed within the active are and receive power wirelessly.

The planar resonator may have additional components coupled to theconductor. Components such as capacitors, inductors, resistors, diodes,and the like may be coupled to the conductor and may be used to adjustor tune the resonant frequency and the impedance matching for theresonators.

A planar resonator structure of the type described above and shown inFIG. 11( a), may be created, for example, with a quality factor, Q, of100 or higher and even Q of 1,000 or higher. Energy may be wirelesslytransferred from one planar resonator structure to another over adistance larger than the characteristic size of the resonators, as shownin FIG. 11( c).

In addition to utilizing magnetic materials to realize a structure withproperties similar to the inductive element in the magnetic resonators,it may be possible to use a combination of good conductor materials andmagnetic material to realize such inductive structures. FIG. 16( a)shows a magnetic resonator structure 1602 that may include one or moreenclosures made of high-conductivity materials (the inside of whichwould be shielded from AC electromagnetic fields generated outside)surrounded by at least one layer of magnetic material and linked byblocks of magnetic material 1604.

A structure may include a high-conductivity sheet of material covered onone side by a layer of magnetic material. The layered structure mayinstead be applied conformally to an electronic device, so that parts ofthe device may be covered by the high-conductivity and magnetic materiallayers, while other parts that need to be easily accessed (such asbuttons or screens) may be left uncovered. The structure may also orinstead include only layers or bulk pieces of magnetic material. Thus, amagnetic resonator may be incorporated into an existing device withoutsignificantly interfering with its existing functions and with little orno need for extensive redesign. Moreover, the layers of good conductorand/or magnetic material may be made thin enough (of the order of amillimeter or less) that they would add little extra weight and volumeto the completed device. An oscillating current applied to a length ofconductor wound around the structure, as shown by the square loop in thecenter of the structure in FIG. 16 may be used to excite theelectromagnetic fields associated with this structure.

Quality Factor of the Structure

A structure of the type described above may be created with a qualityfactor, Q, of the order of 1,000 or higher. This high-Q is possible evenif the losses in the magnetic material are high, if the fraction ofmagnetic energy within the magnetic material is small compared to thetotal magnetic energy associated with the object. For structurescomposed of layers conducting materials and magnetic materials, thelosses in the conducting materials may be reduced by the presence of themagnetic materials as described previously. In structures where themagnetic material layer's thickness is of the order of 1/100 of thelargest dimension of the system (e.g., the magnetic material may be ofthe order of 1 mm thick, while the area of the structure is of the orderof 10 cm×10 cm), and the relative permeability is of the order of 1,000,it is possible to make the fraction of magnetic energy contained withinthe magnetic material only a few hundredths of the total magnetic energyassociated with the object or resonator. To see how that comes about,note that the expression for the magnetic energy contained in a volumeis U_(m)=∝_(V)drB(r)²/(2μ_(r)μ₀), so as long as B (rather than H) is themain field conserved across the magnetic material-air interface (whichis typically the case in open magnetic circuits), the fraction ofmagnetic energy contained in the high-μ_(r) region may be significantlyreduced compared to what it is in air.

If the fraction of magnetic energy in the magnetic material is denotedby frac, and the loss tangent of the material is tan δ, then the Q ofthe resonator, assuming the magnetic material is the only source oflosses, is Q=1/(frac×tan δ). Thus, even for loss tangents as high as0.1, it is possible to achieve Q's of the order of 1,000 for these typesof resonator structures.

If the structure is driven with N turns of wire wound around it, thelosses in the excitation inductor loop can be ignored if N issufficiently high. FIG. 17 shows an equivalent circuit 1700 schematicfor these structures and the scaling of the loss mechanisms andinductance with the number of turns, N, wound around a structure made ofconducting and magnetic material. If proximity effects can be neglected(by using an appropriate winding, or a wire designed to minimizeproximity effects, such as Litz wire and the like), the resistance 1702due to the wire in the looped conductor scales linearly with the lengthof the loop, which is in turn proportional to the number of turns. Onthe other hand, both the equivalent resistance 1708 and equivalentinductance 1704 of these special structures are proportional to thesquare of the magnetic field inside the structure. Since this magneticfield is proportional to N, the equivalent resistance 1708 andequivalent inductance 1704 are both proportional to N². Thus, for largeenough N, the resistance 1702 of the wire is much smaller than theequivalent resistance 1708 of the magnetic structure, and the Q of theresonator asymptotes to Q_(max)=ωL_(μ)/R_(μ).

FIG. 16 (a) shows a drawing of a copper and magnetic material structure1602 driven by a square loop of current around the narrowed segment atthe center of the structure 1604 and the magnetic field streamlinesgenerated by this structure 1608. This exemplary structure includes two20 cm×8 cm×2 cm hollow regions enclosed with copper and then completelycovered with a 2 mm layer of magnetic material having the propertiesμ_(r)′=1,400, μ_(r)″=5, and σ=0.5 S/m. These two parallelepipeds arespaced 4 cm apart and are connected by a 2 cm×4 cm×2 cm block of thesame magnetic material. The excitation loop is wound around the centerof this block. At a frequency of 300 kHz, this structure has acalculated Q of 890. The conductor and magnetic material structure maybe shaped to optimize certain system parameters. For example, the sizeof the structure enclosed by the excitation loop may be small to reducethe resistance of the excitation loop, or it may be large to mitigatelosses in the magnetic material associated with large magnetic fields.Note that the magnetic streamlines and Q's associated with the samestructure composed of magnetic material only would be similar to thelayer conductor and magnetic material design shown here.

Electromagnetic Resonators Interacting with Other Objects

For electromagnetic resonators, extrinsic loss mechanisms that perturbthe intrinsic Q may include absorption losses inside the materials ofnearby extraneous objects and radiation losses related to scattering ofthe resonant fields from nearby extraneous objects. Absorption lossesmay be associated with materials that, over the frequency range ofinterest, have non-zero, but finite, conductivity, σ, (or equivalently anon-zero and finite imaginary part of the dielectric permittivity), suchthat electromagnetic fields can penetrate it and induce currents in it,which then dissipate energy through resistive losses. An object may bedescribed as lossy if it at least partly includes lossy materials.

Consider an object including a homogeneous isotropic material ofconductivity, σ and magnetic permeability, μ. The penetration depth ofelectromagnetic fields inside this object is given by the skin depth,δ=√{square root over (2/ωμσ)}. The power dissipated inside the object,P_(d), can be determined from P_(d)=∫_(V)drσ|E|²=∫_(V)dr|J|²/σ where wemade use of Ohm's law, J=σE, and where E is the electric field and J isthe current density.

If over the frequency range of interest, the conductivity, σ, of thematerial that composes the object is low enough that the material's skindepth, δ, may be considered long, (i.e. δ is longer than the objects'characteristic size, or δ is longer than the characteristic size of theportion of the object that is lossy) then the electromagnetic fields, Eand H, where H is the magnetic field, may penetrate significantly intothe object. Then, these finite-valued fields may give rise to adissipated power that scales as P_(d)˜σV_(ol)

|E|²

, where V_(ol) is the volume of the object that is lossy and

|E|²

is the spatial average of the electric-field squared, in the volumeunder consideration. Therefore, in the low-conductivity limit, thedissipated power scales proportionally to the conductivity and goes tozero in the limit of a non-conducting (purely dielectric) material.

If over the frequency range of interest, the conductivity, σ, of thematerial that composes the object is high enough that the material'sskin depth may be considered short, then the electromagnetic fields, Eand H, may penetrate only a short distance into the object (namely theystay close to the ‘skin’ of the material, where δ is smaller than thecharacteristic thickness of the portion of the object that is lossy). Inthis case, the currents induced inside the material may be concentratedvery close to the material surface, approximately within a skin depth,and their magnitude may be approximated by the product of a surfacecurrent density (mostly determined by the shape of the incidentelectromagnetic fields and, as long as the thickness of the conductor ismuch larger than the skin-depth, independent of frequency andconductivity to first order) K(x, y) (where x and y are coordinatesparameterizing the surface) and a function decaying exponentially intothe surface: exp(−z/δ)/δ (where z denotes the coordinate locally normalto the surface): J(x, y, z)=K(x, y) exp(−z/δ)/δ. Then, the dissipatedpower, P_(d), may be estimated by,P _(d)=^(v) dr|J(r)|²/σ≈(^(s) dxdy|K(x,y)|²)(₀ ^(∞)dzexp(2z/δ)/(σδ²))=√{square root over (μω/8σ)}(^(s) dxdy|K(x,y)|²)

Therefore, in the high-conductivity limit, the dissipated power scalesinverse proportionally to the square-root of the conductivity and goesto zero in the limit of a perfectly-conducting material.

If over the frequency range of interest, the conductivity, σ, of thematerial that composes the object is finite, then the material's skindepth, δ, may penetrate some distance into the object and some amount ofpower may be dissipated inside the object, depending also on the size ofthe object and the strength of the electromagnetic fields. Thisdescription can be generalized to also describe the general case of anobject including multiple different materials with different propertiesand conductivities, such as an object with an arbitrary inhomogeneousand anisotropic distribution of the conductivity inside the object.

Note that the magnitude of the loss mechanisms described above maydepend on the location and orientation of the extraneous objectsrelative to the resonator fields as well as the material composition ofthe extraneous objects. For example, high-conductivity materials mayshift the resonant frequency of a resonator and detune it from otherresonant objects. This frequency shift may be fixed by applying afeedback mechanism to a resonator that corrects its frequency, such asthrough changes in the inductance and/or capacitance of the resonator.These changes may be realized using variable capacitors and inductors,in some cases achieved by changes in the geometry of components in theresonators. Other novel tuning mechanisms, described below, may also beused to change the resonator frequency.

Where external losses are high, the perturbed Q may be low and steps maybe taken to limit the absorption of resonator energy inside suchextraneous objects and materials. Because of the functional dependenceof the dissipated power on the strength of the electric and magneticfields, one might optimize system performance by designing a system sothat the desired coupling is achieved with shorter evanescent resonantfield tails at the source resonator and longer at the device resonator,so that the perturbed Q of the source in the presence of other objectsis optimized (or vice versa if the perturbed Q of the device needs to beoptimized).

Note that many common extraneous materials and objects such as people,animals, plants, building materials, and the like, may have lowconductivities and therefore may have little impact on the wirelessenergy transfer scheme disclosed here. An important fact related to themagnetic resonator designs we describe is that their electric fields maybe confined primarily within the resonator structure itself, so itshould be possible to operate within the commonly accepted guidelinesfor human safety while providing wireless power exchange over mid rangedistances.

Electromagnetic Resonators with Reduced Interactions

One frequency range of interest for near-field wireless powertransmission is between 10 kHz and 100 MHz. In this frequency range, alarge variety of ordinary non-metallic materials, such as for exampleseveral types of wood and plastic may have relatively low conductivity,such that only small amounts of power may be dissipated inside them. Inaddition, materials with low loss tangents, tan Δ, where tan Δ=∈″/∈′,and ∈″ and ∈′ are the imaginary and real parts of the permittivityrespectively, may also have only small amounts of power dissipatedinside them. Metallic materials, such as copper, silver, gold, and thelike, with relatively high conductivity, may also have little powerdissipated in them, because electromagnetic fields are not able tosignificantly penetrate these materials, as discussed earlier. Thesevery high and very low conductivity materials, and low loss tangentmaterials and objects may have a negligible impact on the losses of amagnetic resonator.

However, in the frequency range of interest, there are materials andobjects such as some electronic circuits and some lower-conductivitymetals, which may have moderate (in general inhomogeneous andanisotropic) conductivity, and/or moderate to high loss tangents, andwhich may have relatively high dissipative losses. Relatively largeramounts of power may be dissipated inside them. These materials andobjects may dissipate enough energy to reduce Q_((p)) by non-trivialamounts, and may be referred to as “lossy objects”.

One way to reduce the impact of lossy materials on the Q_((p)) of aresonator is to use high-conductivity materials to shape the resonatorfields such that they avoid the lossy objects. The process of usinghigh-conductivity materials to tailor electromagnetic fields so thatthey avoid lossy objects in their vicinity may be understood byvisualizing high-conductivity materials as materials that deflect orreshape the fields. This picture is qualitatively correct as long as thethickness of the conductor is larger than the skin-depth because theboundary conditions for electromagnetic fields at the surface of a goodconductor force the electric field to be nearly completely perpendicularto, and the magnetic field to be nearly completely tangential to, theconductor surface. Therefore, a perpendicular magnetic field or atangential electric field will be “deflected away” from the conductingsurface. Furthermore, even a tangential magnetic field or aperpendicular electric field may be forced to decrease in magnitude onone side and/or in particular locations of the conducting surface,depending on the relative position of the sources of the fields and theconductive surface.

As an example, FIG. 18 shows a finite element method (FEM) simulation oftwo high conductivity surfaces 1802 above and below a lossy dielectricmaterial 1804 in an external, initially uniform, magnetic field offrequency f=6.78 MHz. The system is azimuthally symmetric around the r=0axis. In this simulation, the lossy dielectric material 1804 issandwiched between two conductors 1802, shown as the white lines atapproximately z=±0.01 m. In the absence of the conducting surfaces aboveand below the dielectric disk, the magnetic field (represented by thedrawn magnetic field lines) would have remained essentially uniform(field lines straight and parallel with the z-axis), indicating that themagnetic field would have passed straight through the lossy dielectricmaterial. In this case, power would have been dissipated in the lossydielectric disk. In the presence of conducting surfaces, however, thissimulation shows the magnetic field is reshaped. The magnetic field isforced to be tangential to surface of the conductor and so is deflectedaround those conducting surfaces 1802, minimizing the amount of powerthat may be dissipated in the lossy dielectric material 1804 behind orbetween the conducting surfaces. As used herein, an axis of electricalsymmetry refers to any axis about which a fixed or time-varyingelectrical or magnetic field is substantially symmetric during anexchange of energy as disclosed herein.

A similar effect is observed even if only one conducting surface, aboveor below, the dielectric disk, is used. If the dielectric disk is thin,the fact that the electric field is essentially zero at the surface, andcontinuous and smooth close to it, means that the electric field is verylow everywhere close to the surface (i.e. within the dielectric disk). Asingle surface implementation for deflecting resonator fields away fromlossy objects may be preferred for applications where one is not allowedto cover both sides of the lossy material or object (e.g. an LCDscreen). Note that even a very thin surface of conducting material, onthe order of a few skin-depths, may be sufficient (the skin depth inpure copper at 6.78 MHz is ˜20 μm, and at 250 kHz is ˜100 μm) tosignificantly improve the Q_((p)) of a resonator in the presence oflossy materials.

Lossy extraneous materials and objects may be parts of an apparatus, inwhich a high-Q resonator is to be integrated. The dissipation of energyin these lossy materials and objects may be reduced by a number oftechniques including:

-   -   by positioning the lossy materials and objects away from the        resonator, or, in special positions and orientations relative to        the resonator.    -   by using a high conductivity material or structure to partly or        entirely cover lossy materials and objects in the vicinity of a        resonator    -   by placing a closed surface (such as a sheet or a mesh) of        high-conductivity material around a lossy object to completely        cover the lossy object and shape the resonator fields such that        they avoid the lossy object.    -   by placing a surface (such as a sheet or a mesh) of a        high-conductivity material around only a portion of a lossy        object, such as along the top, the bottom, along the side, and        the like, of an object or material.    -   by placing even a single surface (such as a sheet or a mesh) of        high-conductivity material above or below or on one side of a        lossy object to reduce the strength of the fields at the        location of the lossy object.

FIG. 19 shows a capacitively-loaded loop inductor forming a magneticresonator 102 and a disk-shaped surface of high-conductivity material1802 that completely surrounds a lossy object 1804 placed inside theloop inductor. Note that some lossy objects may be components, such aselectronic circuits, that may need to interact with, communicate with,or be connected to the outside environment and thus cannot be completelyelectromagnetically isolated. Partially covering a lossy material withhigh conductivity materials may still reduce extraneous losses whileenabling the lossy material or object to function properly.

FIG. 20 shows a capacitively-loaded loop inductor that is used as theresonator 102 and a surface of high-conductivity material 1802,surrounding only a portion of a lossy object 1804, that is placed insidethe inductor loop.

Extraneous losses may be reduced, but may not be completely eliminated,by placing a single surface of high-conductivity material above, below,on the side, and the like, of a lossy object or material. An example isshown in FIG. 21, where a capacitively-loaded loop inductor is used asthe resonator 102 and a surface of high-conductivity material 1802 isplaced inside the inductor loop under a lossy object 1804 to reduce thestrength of the fields at the location of the lossy object. It may bepreferable to cover only one side of a material or object because ofconsiderations of cost, weight, assembly complications, air flow, visualaccess, physical access, and the like.

A single surface of high-conductivity material may be used to avoidobjects that cannot or should not be covered from both sides (e.g. LCDor plasma screens). Such lossy objects may be avoided using opticallytransparent conductors. High-conductivity optically opaque materials mayinstead be placed on only a portion of the lossy object, instead of, orin addition to, optically transparent conductors. The adequacy ofsingle-sided vs. multi-sided covering implementations, and the designtrade-offs inherent therein may depend on the details of the wirelessenergy transfer scenario and the properties of the lossy materials andobjects.

Below we describe an example using high-conductivity surfaces to improvethe Q-insensitivity, Θ_((p)), of an integrated magnetic resonator usedin a wireless energy-transfer system. FIG. 22 shows a wireless projector2200. The wireless projector may include a device resonator 102C, aprojector 2202, a wireless network/video adapter 2204, and powerconversion circuits 2208, arranged as shown. The device resonator 102Cmay include a three-turn conductor loop, arranged to enclose a surface,and a capacitor network 2210. The conductor loop may be designed so thatthe device resonator 102C has a high Q (e.g., >100) at its operatingresonant frequency. Prior to integration in the completely wirelessprojector 2200, this device resonator 102C has a Q of approximately 477at the designed operating resonant frequency of 6.78 MHz. Uponintegration, and placing the wireless network/video adapter card 2204 inthe center of the resonator loop inductor, the resonatorQ_((integrated)) was decreased to approximately 347. At least some ofthe reduction from Q to Q_((integrated)) was attributed to losses in theperturbing wireless network/video adapter card. As described above,electromagnetic fields associated with the magnetic resonator 102C mayinduce currents in and on the wireless network/video adapter card 2204,which may be dissipated in resistive losses in the lossy materials thatcompose the card. We observed that Q_((integrated)) of the resonator maybe impacted differently depending on the composition, position, andorientation, of objects and materials placed in its vicinity.

In a completely wireless projector example, covering the network/videoadapter card with a thin copper pocket (a folded sheet of copper thatcovered the top and the bottom of the wireless network/video adaptercard, but not the communication antenna) improved the Q_((integrated))of the magnetic resonator to a Q_((integrated+copper pocket)) ofapproximately 444. In other words, most of the reduction inQ_((integrated)) due to the perturbation caused by the extraneousnetwork/video adapter card could be eliminated using a copper pocket todeflect the resonator fields away from the lossy materials.

In another completely wireless projector example, covering thenetwork/video adapter card with a single copper sheet placed beneath thecard provided a Q_((integrated+copper sheet)) approximately equal toQ_((integrated+copper pocket)). In that example, the high perturbed Q ofthe system could be maintained with a single high-conductivity sheetused to deflect the resonator fields away from the lossy adapter card.

It may be advantageous to position or orient lossy materials or objects,which are part of an apparatus including a high-Q electromagneticresonator, in places where the fields produced by the resonator arerelatively weak, so that little or no power may be dissipated in theseobjects and so that the Q-insensitivity, Θ_((p)), may be large. As wasshown earlier, materials of different conductivity may responddifferently to electric versus magnetic fields. Therefore, according tothe conductivity of the extraneous object, the positioning technique maybe specialized to one or the other field.

FIG. 23 shows the magnitude of the electric 2312 and magnetic fields2314 along a line that contains the diameter of the circular loopinductor and the electric 2318 and magnetic fields 2320 along the axisof the loop inductor for a capacitively-loaded circular loop inductor ofwire of radius 30 cm, resonant at 10 MHz. It can be seen that theamplitude of the resonant near-fields reach their maxima close to thewire and decay away from the loop, 2312, 2314. In the plane of the loopinductor 2318, 2320, the fields reach a local minimum at the center ofthe loop. Therefore, given the finite size of the apparatus, it may bethat the fields are weakest at the extrema of the apparatus or it may bethat the field magnitudes have local minima somewhere within theapparatus. This argument holds for any other type of electromagneticresonator 102 and any type of apparatus. Examples are shown in FIGS. 24a and 24 b, where a capacitively-loaded inductor loop forms a magneticresonator 102 and an extraneous lossy object 1804 is positioned wherethe electromagnetic fields have minimum magnitude.

In a demonstration example, a magnetic resonator was formed using athree-turn conductor loop, arranged to enclose a square surface (withrounded corners), and a capacitor network. The Q of the resonator wasapproximately 619 at the designed operating resonant frequency of 6.78MHz. The perturbed Q of this resonator depended on the placement of theperturbing object, in this case a pocket projector, relative to theresonator. When the perturbing projector was located inside the inductorloop and at its center or on top of the inductor wire turns,Q_((projector)) was approximately 96, lower than when the perturbingprojector was placed outside of the resonator, in which caseQ_((projector)) was approximately 513. These measurements support theanalysis that shows the fields inside the inductor loop may be largerthan those outside it, so lossy objects placed inside such a loopinductor may yield lower perturbed Q's for the system than when thelossy object is placed outside the loop inductor. Depending on theresonator designs and the material composition and orientation of thelossy object, the arrangement shown in FIG. 24 b may yield a higherQ-insensitivity, Θ_((projector)) than the arrangement shown in FIG. 24a.

High-Q resonators may be integrated inside an apparatus. Extraneousmaterials and objects of high dielectric permittivity, magneticpermeability, or electric conductivity may be part of the apparatus intowhich a high-Q resonator is to be integrated. For these extraneousmaterials and objects in the vicinity of a high-Q electromagneticresonator, depending on their size, position and orientation relative tothe resonator, the resonator field-profile may be distorted and deviatesignificantly from the original unperturbed field-profile of theresonator. Such a distortion of the unperturbed fields of the resonatormay significantly decrease the Q to a lower Q_((p)), even if theextraneous objects and materials are lossless.

It may be advantageous to position high-conductivity objects, which arepart of an apparatus including a high-Q electromagnetic resonator, atorientations such that the surfaces of these objects are, as much aspossible, perpendicular to the electric field lines produced by theunperturbed resonator and parallel to the magnetic field lines producedby the unperturbed resonator, thus distorting the resonant fieldprofiles by the smallest amount possible. Other common objects that maybe positioned perpendicular to the plane of a magnetic resonator loopinclude screens (LCD, plasma, etc), batteries, cases, connectors,radiative antennas, and the like. The Q-insensitivity, Θ_((p)), of theresonator may be much larger than if the objects were positioned at adifferent orientation with respect to the resonator fields.

Lossy extraneous materials and objects, which are not part of theintegrated apparatus including a high-Q resonator, may be located orbrought in the vicinity of the resonator, for example, during the use ofthe apparatus. It may be advantageous in certain circumstances to usehigh conductivity materials to tailor the resonator fields so that theyavoid the regions where lossy extraneous objects may be located orintroduced to reduce power dissipation in these materials and objectsand to increase Q-insensitivity, Θ_((p)). An example is shown in FIG.25, where a capacitively-loaded loop inductor and capacitor are used asthe resonator 102 and a surface of high-conductivity material 1802 isplaced above the inductor loop to reduce the magnitude of the fields inthe region above the resonator, where lossy extraneous objects 1804 maybe located or introduced.

Note that a high-conductivity surface brought in the vicinity of aresonator to reshape the fields may also lead to Q_((cond. surface))<Q.The reduction in the perturbed Q may be due to the dissipation of energyinside the lossy conductor or to the distortion of the unperturbedresonator field profiles associated with matching the field boundaryconditions at the surface of the conductor. Therefore, while ahigh-conductivity surface may be used to reduce the extraneous lossesdue to dissipation inside an extraneous lossy object, in some cases,especially in some of those where this is achieved by significantlyreshaping the electromagnetic fields, using such a high-conductivitysurface so that the fields avoid the lossy object may result effectivelyin Q_((p+cond. surface))<Q_((p)) rather than the desired resultQ_((p+cond. surface))>Q_((p)).

As described above, in the presence of loss inducing objects, theperturbed quality factor of a magnetic resonator may be improved if theelectromagnetic fields associated with the magnetic resonator arereshaped to avoid the loss inducing objects. Another way to reshape theunperturbed resonator fields is to use high permeability materials tocompletely or partially enclose or cover the loss inducing objects,thereby reducing the interaction of the magnetic field with the lossinducing objects.

Magnetic field shielding has been described previously, for example inElectrodynamics 3^(rd) Ed., Jackson, pp. 201-203. There, a sphericalshell of magnetically permeable material was shown to shield itsinterior from external magnetic fields. For example, if a shell of innerradius a, outer radius b, and relative permeability y_(r), is placed inan initially uniform magnetic field H₀, then the field inside the shellwill have a constant magnitude, 9μ_(r)H₀/[(2μ_(r)+1)(μ_(r)+2)−2(a/b)³(μ_(r)−1)²], which tends to 9H₀/2μ_(r)(1−a/b)³) if μ_(r)>>1. This resultshows that an incident magnetic field (but not necessarily an incidentelectric field) may be greatly attenuated inside the shell, even if theshell is quite thin, provided the magnetic permeability is high enough.It may be advantageous in certain circumstances to use high permeabilitymaterials to partly or entirely cover lossy materials and objects sothat they are avoided by the resonator magnetic fields and so thatlittle or no power is dissipated in these materials and objects. In suchan approach, the Q-insensitivity, Θ_((p)), may be larger than if thematerials and objects were not covered, possibly larger than 1.

It may be desirable to keep both the electric and magnetic fields awayfrom loss inducing objects. As described above, one way to shape thefields in such a manner is to use high-conductivity surfaces to eithercompletely or partially enclose or cover the loss inducing objects. Alayer of magnetically permeable material, also referred to as magneticmaterial, (any material or meta-material having a non-trivial magneticpermeability), may be placed on or around the high-conductivitysurfaces. The additional layer of magnetic material may present a lowerreluctance path (compared to free space) for the deflected magneticfield to follow and may partially shield the electric conductorunderneath it from the incident magnetic flux. This arrangement mayreduce the losses due to induced currents in the high-conductivitysurface. Under some circumstances the lower reluctance path presented bythe magnetic material may improve the perturbed Q of the structure.

FIG. 26 a shows an axially symmetric FEM simulation of a thin conducting2604 (copper) disk (20 cm in diameter, 2 cm in height) exposed to aninitially uniform, externally applied magnetic field (gray flux lines)along the z-axis. The axis of symmetry is at r=0. The magneticstreamlines shown originate at z=−∞, where they are spaced from r=3 cmto r=10 cm in intervals of 1 cm. The axes scales are in meters. Imagine,for example, that this conducing cylinder encloses loss-inducing objectswithin an area circumscribed by a magnetic resonator in a wirelessenergy transfer system such as shown in FIG. 19.

This high-conductivity enclosure may increase the perturbing Q of thelossy objects and therefore the overall perturbed Q of the system, butthe perturbed Q may still be less than the unperturbed Q because ofinduced losses in the conducting surface and changes to the profile ofthe electromagnetic fields. Decreases in the perturbed Q associated withthe high-conductivity enclosure may be at least partially recovered byincluding a layer of magnetic material along the outer surface orsurfaces of the high-conductivity enclosure. FIG. 26 b shows an axiallysymmetric FEM simulation of the thin conducting 2604A (copper) disk (20cm in diameter, 2 cm in height) from FIG. 26 a, but with an additionallayer of magnetic material placed directly on the outer surface of thehigh-conductivity enclosure. Note that the presence of the magneticmaterial may provide a lower reluctance path for the magnetic field,thereby at least partially shielding the underlying conductor andreducing losses due to induced eddy currents in the conductor.

FIG. 27 depicts a variation (in axi-symmetric view) to the system shownin FIG. 26 where not all of the lossy material 2708 may be covered by ahigh-conductivity surface 2706. In certain circumstances it may beuseful to cover only one side of a material or object, such as due toconsiderations of cost, weight, assembly complications, air flow, visualaccess, physical access, and the like. In the exemplary arrangementshown in FIG. 27, only one surface of the lossy material 2708 is coveredand the resonator inductor loop is placed on the opposite side of thehigh-conductivity surface.

Mathematical models were used to simulate a high-conductivity enclosuremade of copper and shaped like a 20 cm diameter by 2 cm high cylindricaldisk placed within an area circumscribed by a magnetic resonator whoseinductive element was a single-turn wire loop with loop radius r=11 cmand wire radius a=1 mm. Simulations for an applied 6.78 MHzelectromagnetic field suggest that the perturbing quality factor of thishigh-conductivity enclosure, δQ_((enclosure)), is 1,870. When thehigh-conductivity enclosure was modified to include a 0.25 cm-thicklayer of magnetic material with real relative permeability, μ_(r)′40,and imaginary relative permeability, μ_(r)″=10⁻², simulations suggestthe perturbing quality factor is increased toδQ_((enclosure+magnetic material))=5,060.

The improvement in performance due to the addition of thin layers ofmagnetic material 2702 may be even more dramatic if thehigh-conductivity enclosure fills a larger portion of the areacircumscribed by the resonator's loop inductor 2704. In the exampleabove, if the radius of the inductor loop 2704 is reduced so that it isonly 3 mm away from the surface of the high-conductivity enclosure, theperturbing quality factor may be improved from 670 (conducting enclosureonly) to 2,730 (conducting enclosure with a thin layer of magneticmaterial) by the addition of a thin layer of magnetic material 2702around the outside of the enclosure.

The resonator structure may be designed to have highly confined electricfields, using shielding, or distributed capacitors, for example, whichmay yield high, even when the resonator is very close to materials thatwould typically induce loss.

Coupled Electromagnetic Resonators

The efficiency of energy transfer between two resonators may bedetermined by the strong-coupling figure-of-merit, U=κ/√{square rootover (Γ_(s)Γ_(d))}=(2κ/√{square root over (ω_(s)ω_(d))})√{square rootover (Q_(s)Q_(d))}. In magnetic resonator implementations the couplingfactor between the two resonators may be related to the inductance ofthe inductive elements in each of the resonators, L₁ and L₂, and themutual inductance, M, between them by κ₁₂=ωM/2√{square root over(L₁L₂)}. Note that this expression assumes there is negligible couplingthrough electric-dipole coupling. For capacitively-loaded inductor loopresonators where the inductor loops are formed by circular conductingloops with N turns, separated by a distance D, and oriented as shown inFIG. 1( b), the mutual inductance is M=π/4·μ_(o)N₁N₂(x₁x₂)²/D³ where x₁,N₁ and x₂, N₂ are the characteristic size and number of turns of theconductor loop of the first and second resonators respectively. Notethat this is a quasi-static result, and so assumes that the resonator'ssize is much smaller than the wavelength and the resonators' distance ismuch smaller than the wavelength, but also that their distance is atleast a few times their size. For these circular resonators operated inthe quasi-static limit and at mid-range distances, as described above,k=2κ/√{square root over (ω₁ω₂)}˜(√{square root over (x₁x₂)}/D)³. Strongcoupling (a large U) between resonators at mid-range distances may beestablished when the quality factors of the resonators are large enoughto compensate for the small k at mid-range distances

For electromagnetic resonators, if the two resonators include conductingparts, the coupling mechanism may be that currents are induced on oneresonator due to electric and magnetic fields generated from the other.The coupling factor may be proportional to the flux of the magneticfield produced from the high-Q inductive element in one resonatorcrossing a closed area of the high-Q inductive element of the secondresonator.

Coupled Electromagnetic Resonators with Reduced Interactions

As described earlier, a high-conductivity material surface may be usedto shape resonator fields such that they avoid lossy objects, p, in thevicinity of a resonator, thereby reducing the overall extraneous lossesand maintaining a high Q-insensitivity Θ_((p+cond.surface)) of theresonator. However, such a surface may also lead to a perturbed couplingfactor, k_(p+cond. surface)), between resonators that is smaller thanthe perturbed coupling factor, k_((p)) and depends on the size,position, and orientation of the high-conductivity material relative tothe resonators. For example, if high-conductivity materials are placedin the plane and within the area circumscribed by the inductive elementof at least one of the magnetic resonators in a wireless energy transfersystem, some of the magnetic flux through the area of the resonator,mediating the coupling, may be blocked and k may be reduced.

Consider again the example of FIG. 19. In the absence of thehigh-conductivity disk enclosure, a certain amount of the externalmagnetic flux may cross the circumscribed area of the loop. In thepresence of the high-conductivity disk enclosure, some of this magneticflux may be deflected or blocked and may no longer cross the area of theloop, thus leading to a smaller perturbed coupling factork_(12(p+cond. surfaces)). However, because the deflected magnetic-fieldlines may follow the edges of the high-conductivity surfaces closely,the reduction in the flux through the loop circumscribing the disk maybe less than the ratio of the areas of the face of the disk to the areaof the loop.

One may use high-conductivity material structures, either alone, orcombined with magnetic materials to optimize perturbed quality factors,perturbed coupling factors, or perturbed efficiencies.

Consider the example of FIG. 21. Let the lossy object have a size equalto the size of the capacitively-loaded inductor loop resonator, thusfilling its area A 2102. A high-conductivity surface 1802 may be placedunder the lossy object 1804. Let this be resonator 1 in a system of twocoupled resonators 1 and 2, and let us consider howU_(12(object+cond. surface)) scales compared to U₁₂ as the area A_(s)2104 of the conducting surface increases. Without the conducting surface1802 below the lossy object 1804, the k-insensitivity, β_(12(object)),may be approximately one, but the Q-insensitivity, Θ_(1(object)), may besmall, so the U-insensitivity Ξ_(12(object)) may be small.

Where the high-conductivity surface below the lossy object covers theentire area of the inductor loop resonator (A=A),k_(12(object+cond. surface)) may approach zero, because little flux isallowed to cross the inductor loop, so U_(12(object+cond. surface)) mayapproach zero. For intermediate sizes of the high-conductivity surface,the suppression of extrinsic losses and the associated Q-insensitivity,Ξ_(1(object+cond surface)), may be large enough compared toΘ_(1(object)), while the reduction in coupling may not be significantand the associated k-insensitivity, β_(12(object+cond. surface)), may benot much smaller than β_(12(object)), so that the overallU_(12(object+cond. surface)) may be increased compared toU_(12(object)). The optimal degree of avoiding of extraneous lossyobjects via high-conductivity surfaces in a system of wireless energytransfer may depend on the details of the system configuration and theapplication.

We describe using high-conductivity materials to either completely orpartially enclose or cover loss inducing objects in the vicinity ofhigh-Q resonators as one potential method to achieve high perturbed Q'sfor a system. However, using a good conductor alone to cover the objectsmay reduce the coupling of the resonators as described above, therebyreducing the efficiency of wireless power transfer. As the area of theconducting surface approaches the area of the magnetic resonator, forexample, the perturbed coupling factor, k_((p)), may approach zero,making the use of the conducting surface incompatible with efficientwireless power transfer.

One approach to addressing the aforementioned problem is to place alayer of magnetic material around the high-conductivity materialsbecause the additional layer of permeable material may present a lowerreluctance path (compared to free space) for the deflected magneticfield to follow and may partially shield the electric conductorunderneath it from incident magnetic flux. Under some circumstances thelower reluctance path presented by the magnetic material may improve theelectromagnetic coupling of the resonator to other resonators. Decreasesin the perturbed coupling factor associated with using conductingmaterials to tailor resonator fields so that they avoid lossy objects inand around high-Q magnetic resonators may be at least partiallyrecovered by including a layer of magnetic material along the outersurface or surfaces of the conducting materials. The magnetic materialsmay increase the perturbed coupling factor relative to its initialunperturbed value.

Note that the simulation results in FIG. 26 show that an incidentmagnetic field may be deflected less by a layered magnetic material andconducting structure than by a conducting structure alone. If a magneticresonator loop with a radius only slightly larger than that of the disksshown in FIGS. 26( a) and 26(b) circumscribed the disks, it is clearthat more flux lines would be captured in the case illustrated in FIG.26( b) than in FIG. 26( a), and therefore k_((disk)) would be larger forthe case illustrated in FIG. 26( b). Therefore, including a layer ofmagnetic material on the conducting material may improve the overallsystem performance. System analyses may be performed to determinewhether these materials should be partially, totally, or minimallyintegrated into the resonator.

As described above, FIG. 27 depicts a layered conductor 2706 andmagnetic material 2702 structure that may be appropriate for use whennot all of a lossy material 2708 may be covered by a conductor and/ormagnetic material structure. It was shown earlier that for a copperconductor disk with a 20 cm diameter and a 2 cm height, circumscribed bya resonator with an inductor loop radius of 11 cm and a wire radius a=1mm, the calculated perturbing Q for the copper cylinder was 1,870. Ifthe resonator and the conducting disk shell are placed in a uniformmagnetic field (aligned along the axis of symmetry of the inductorloop), we calculate that the copper conductor has an associated couplingfactor insensitivity of 0.34. For comparison, we model the samearrangement but include a 0.25 cm-thick layer of magnetic material witha real relative permeability, μ_(r)′=40, and an imaginary relativepermeability, μ_(r)″=10⁻². Using the same model and parameters describedabove, we find that the coupling factor insensitivity is improved to0.64 by the addition of the magnetic material to the surface of theconductor.

Magnetic materials may be placed within the area circumscribed by themagnetic resonator to increase the coupling in wireless energy transfersystems. Consider a solid sphere of a magnetic material with relativepermeability, μ_(r), placed in an initially uniform magnetic field. Inthis example, the lower reluctance path offered by the magnetic materialmay cause the magnetic field to concentrate in the volume of the sphere.We find that the magnetic flux through the area circumscribed by theequator of the sphere is enhanced by a factor of 3μ_(r)/(μ_(r)+2), bythe addition of the magnetic material. If μ_(r)>>1, this enhancementfactor may be close to 3.

One can also show that the dipole moment of a system comprising themagnetic sphere circumscribed by the inductive element in a magneticresonator would have its magnetic dipole enhanced by the same factor.Thus, the magnetic sphere with high permeability practically triples thedipole magnetic coupling of the resonator. It is possible to keep mostof this increase in coupling if we use a spherical shell of magneticmaterial with inner radius a, and outer radius b, even if this shell ison top of block or enclosure made from highly conducting materials. Inthis case, the enhancement in the flux through the equator is

$\frac{3{\mu_{r}\left( {1 - \left( \frac{a}{b} \right)^{3}} \right)}}{{\mu_{r}\left( {1 - \left( \frac{a}{b} \right)^{3}} \right)} + {2\left( {1 + {\frac{1}{2}\left( \frac{a}{b} \right)^{3}}} \right)}}.$For μ_(r)=1,000 and (a/b)=0.99, this enhancement factor is still 2.73,so it possible to significantly improve the coupling even with thinlayers of magnetic material.

As described above, structures containing magnetic materials may be usedto realize magnetic resonators. FIG. 16( a) shows a 3 dimensional modelof a copper and magnetic material structure 1600 driven by a square loopof current around the choke point at its center. FIG. 16( b) shows theinteraction, indicated by magnetic field streamlines, between twoidentical structures 1600A-B with the same properties as the one shownin FIG. 16( a). Because of symmetry, and to reduce computationalcomplexity, only one half of the system is modeled. If we fix therelative orientation between the two objects and vary theircenter-to-center distance (the image shown is at a relative separationof 50 cm), we find that, at 300 kHz, the coupling efficiency varies from87% to 55% as the separation between the structures varies from 30 cm to60 cm. Each of the example structures shown 1600 A-B includes two 20cm×8 cm×2 cm parallelepipeds made of copper joined by a 4 cm×4 cm×2 cmblock of magnetic material and entirely covered with a 2 mm layer of thesame magnetic material (assumed to have μ_(r)=1,400+j5). Resistivelosses in the driving loop are ignored. Each structure has a calculatedQ of 815.

Electromagnetic Resonators and Impedance Matching

Impedance Matching Architectures for Low-Loss Inductive Elements

For purposes of the present discussion, an inductive element may be anycoil or loop structure (the ‘loop’) of any conducting material, with orwithout a (gapped or ungapped) core made of magnetic material, which mayalso be coupled inductively or in any other contactless way to othersystems. The element is inductive because its impedance, including boththe impedance of the loop and the so-called ‘reflected’ impedances ofany potentially coupled systems, has positive reactance, X, andresistance, R.

Consider an external circuit, such as a driving circuit or a driven loador a transmission line, to which an inductive element may be connected.The external circuit (e.g. a driving circuit) may be delivering power tothe inductive element and the inductive element may be delivering powerto the external circuit (e.g. a driven load). The efficiency and amountof power delivered between the inductive element and the externalcircuit at a desired frequency may depend on the impedance of theinductive element relative to the properties of the external circuit.Impedance-matching networks and external circuit control techniques maybe used to regulate the power delivery between the external circuit andthe inductive element, at a desired frequency, f.

The external circuit may be a driving circuit configured to form aamplifier of class A, B, C, D, DE, E, F and the like, and may deliverpower at maximum efficiency (namely with minimum losses within thedriving circuit) when it is driving a resonant network with specificimpedance Z_(o)*, where Z_(o) may be complex and * denotes complexconjugation. The external circuit may be a driven load configured toform a rectifier of class A, B, C, D, DE, E, F and the like, and mayreceive power at maximum efficiency (namely with minimum losses withinthe driven load) when it is driven by a resonant network with specificimpedance Z_(o)*, where Z_(o) may be complex. The external circuit maybe a transmission line with characteristic impedance, Z_(o), and mayexchange power at maximum efficiency (namely with zero reflections) whenconnected to an impedance Z_(o)*. We will call the characteristicimpedance Z_(o) of an external circuit the complex conjugate of theimpedance that may be connected to it for power exchange at maximumefficiency.

Typically the impedance of an inductive element, R+jX, may be muchdifferent from Z_(o)*. For example, if the inductive element has lowloss (a high X/R), its resistance, R, may be much lower than the realpart of the characteristic impedance, Z₀, of the external circuit.Furthermore, an inductive element by itself may not be a resonantnetwork. An impedance-matching network connected to an inductive elementmay typically create a resonant network, whose impedance may beregulated.

Therefore, an impedance-matching network may be designed to maximize theefficiency of the power delivered between the external circuit and theinductive element (including the reflected impedances of any coupledsystems). The efficiency of delivered power may be maximized by matchingthe impedance of the combination of an impedance-matching network and aninductive element to the characteristic impedance of an external circuit(or transmission line) at the desired frequency.

An impedance-matching network may be designed to deliver a specifiedamount of power between the external circuit and the inductive element(including the reflected impedances of any coupled systems). Thedelivered power may be determined by adjusting the complex ratio of theimpedance of the combination of the impedance-matching network and theinductive element to the impedance of the external circuit (ortransmission line) at the desired frequency.

Impedance-matching networks connected to inductive elements may createmagnetic resonators. For some applications, such as wireless powertransmission using strongly-coupled magnetic resonators, a high Q may bedesired for the resonators. Therefore, the inductive element may bechosen to have low losses (high X/R).

Since the matching circuit may typically include additional sources ofloss inside the resonator, the components of the matching circuit mayalso be chosen to have low losses. Furthermore, in high-powerapplications and/or due to the high resonator Q, large currents may runin parts of the resonator circuit and large voltages may be presentacross some circuit elements within the resonator. Such currents andvoltages may exceed the specified tolerances for particular circuitelements and may be too high for particular components to withstand. Insome cases, it may be difficult to find or implement components, such astunable capacitors for example, with size, cost and performance (lossand current/voltage-rating) specifications sufficient to realize high-Qand high-power resonator designs for certain applications. We disclosematching circuit designs, methods, implementations and techniques thatmay preserve the high Q for magnetic resonators, while reducing thecomponent requirements for low loss and/or high current/voltage-rating.

Matching-circuit topologies may be designed that minimize the loss andcurrent-rating requirements on some of the elements of the matchingcircuit. The topology of a circuit matching a low-loss inductive elementto an impedance, Z₀, may be chosen so that some of its components lieoutside the associated high-Q resonator by being in series with theexternal circuit. The requirements for low series loss or highcurrent-ratings for these components may be reduced. Relieving the lowseries loss and/or high-current-rating requirement on a circuit elementmay be particularly useful when the element needs to be variable and/orto have a large voltage-rating and/or low parallel loss.

Matching-circuit topologies may be designed that minimize the voltagerating requirements on some of the elements of the matching circuit. Thetopology of a circuit matching a low-loss inductive element to animpedance, Z₀, may be chosen so that some of its components lie outsidethe associated high-Q resonator by being in parallel with Z₀. Therequirements for low parallel loss or high voltage-rating for thesecomponents may be reduced. Relieving the low parallel loss and/orhigh-voltage requirement on a circuit element may be particularly usefulwhen the element needs to be variable and/or to have a largecurrent-rating and/or low series loss.

The topology of the circuit matching a low-loss inductive element to anexternal characteristic impedance, Z₀, may be chosen so that the fieldpattern of the associated resonant mode and thus its high Q arepreserved upon coupling of the resonator to the external impedance.Otherwise inefficient coupling to the desired resonant mode may occur(potentially due to coupling to other undesired resonant modes),resulting in an effective lowering of the resonator Q.

For applications where the low-loss inductive element or the externalcircuit, may exhibit variations, the matching circuit may need to beadjusted dynamically to match the inductive element to the externalcircuit impedance, Z₀, at the desired frequency, f. Since there maytypically be two tuning objectives, matching or controlling both thereal and imaginary part of the impedance level, Z₀, at the desiredfrequency, f, there may be two variable elements in the matchingcircuit. For inductive elements, the matching circuit may need toinclude at least one variable capacitive element.

A low-loss inductive element may be matched by topologies using twovariable capacitors, or two networks of variable capacitors. A variablecapacitor may, for example, be a tunable butterfly-type capacitorhaving, e.g., a center terminal for connection to a ground or other leadof a power source or load, and at least one other terminal across whicha capacitance of the tunable butterfly-type capacitor can be varied ortuned, or any other capacitor having a user-configurable, variablecapacitance.

A low-loss inductive element may be matched by topologies using one, ora network of, variable capacitor(s) and one, or a network of, variableinductor(s).

A low-loss inductive element may be matched by topologies using one, ora network of, variable capacitor(s) and one, or a network of, variablemutual inductance(s), which transformer-couple the inductive elementeither to an external circuit or to other systems.

In some cases, it may be difficult to find or implement tunable lumpedelements with size, cost and performance specifications sufficient torealize high-Q, high-power, and potentially high-speed, tunableresonator designs. The topology of the circuit matching a variableinductive element to an external circuit may be designed so that some ofthe variability is assigned to the external circuit by varying thefrequency, amplitude, phase, waveform, duty cycle, and the like, of thedrive signals applied to transistors, diodes, switches and the like, inthe external circuit.

The variations in resistance, R, and inductance, L, of an inductiveelement at the resonant frequency may be only partially compensated ornot compensated at all. Adequate system performance may thus bepreserved by tolerances designed into other system components orspecifications. Partial adjustments, realized using fewer tunablecomponents or less capable tunable components, may be sufficient.

Matching-circuit architectures may be designed that achieve the desiredvariability of the impedance matching circuit under high-powerconditions, while minimizing the voltage/current rating requirements onits tunable elements and achieving a finer (i.e. more precise, withhigher resolution) overall tunability. The topology of the circuitmatching a variable inductive element to an impedance, Z₀, may includeappropriate combinations and placements of fixed and variable elements,so that the voltage/current requirements for the variable components maybe reduced and the desired tuning range may be covered with finer tuningresolution. The voltage/current requirements may be reduced oncomponents that are not variable.

The disclosed impedance matching architectures and techniques may beused to achieve the following:

-   -   To maximize the power delivered to, or to minimize impedance        mismatches between, the source low-loss inductive elements (and        any other systems wirelessly coupled to them) from the power        driving generators.    -   To maximize the power delivered from, or to minimize impedance        mismatches between, the device low-loss inductive elements (and        any other systems wirelessly coupled to them) to the power        driven loads.    -   To deliver a controlled amount of power to, or to achieve a        certain impedance relationship between, the source low-loss        inductive elements (and any other systems wirelessly coupled to        them) from the power driving generators.    -   To deliver a controlled amount of power from, or to achieve a        certain impedance relationship between, the device low-loss        inductive elements (and any other systems wirelessly coupled to        them) to the power driven loads.

Topologies for Preservation of Mode Profile (High-Q)

The resonator structure may be designed to be connected to the generatoror the load wirelessly (indirectly) or with a hard-wired connection(directly).

Consider a general indirectly coupled matching topology such as thatshown by the block diagram in FIG. 28( a). There, an inductive element2802, labeled as (R,L) and represented by the circuit symbol for aninductor, may be any of the inductive elements discussed in thisdisclosure or in the references provided herein, and where animpedance-matching circuit 2402 includes or consists of parts A and B. Bmay be the part of the matching circuit that connects the impedance2804, Z₀, to the rest of the circuit (the combination of A and theinductive element (A+(R,L)) via a wireless connection (an inductive orcapacitive coupling mechanism).

The combination of A and the inductive element 2802 may form a resonator102, which in isolation may support a high-Q resonator electromagneticmode, with an associated current and charge distribution. The lack of awired connection between the external circuit, Z₀ and B, and theresonator, A+(R,L), may ensure that the high-Q resonator electromagneticmode and its current/charge distributions may take the form of itsintrinsic (in-isolation) profile, so long as the degree of wirelesscoupling is not too large. That is, the electromagnetic mode,current/charge distributions, and thus the high-Q of the resonator maybe automatically maintained using an indirectly coupled matchingtopology.

This matching topology may be referred to as indirectly coupled, ortransformer-coupled, or inductively-coupled, in the case where inductivecoupling is used between the external circuit and the inductor loop.This type of coupling scenario was used to couple the power supply tothe source resonator and the device resonator to the light bulb in thedemonstration of wireless energy transfer over mid-range distancesdescribed in the referenced Science article.

Next consider examples in which the inductive element may include theinductive element and any indirectly coupled systems. In this case, asdisclosed above, and again because of the lack of a wired connectionbetween the external circuit or the coupled systems and the resonator,the coupled systems may not, with good approximation for not-too-largedegree of indirect coupling, affect the resonator electromagnetic modeprofile and the current/charge distributions of the resonator.Therefore, an indirectly-coupled matching circuit may work equally wellfor any general inductive element as part of a resonator as well as forinductive elements wirelessly-coupled to other systems, as definedherein. Throughout this disclosure, the matching topologies we discloserefer to matching topologies for a general inductive element of thistype, that is, where any additional systems may be indirectly coupled tothe low-loss inductive element, and it is to be understood that thoseadditional systems do not greatly affect the resonator electromagneticmode profile and the current/charge distributions of the resonator.

Based on the argument above, in a wireless power transmission system ofany number of coupled source resonators, device resonators andintermediate resonators the wireless magnetic (inductive) couplingbetween resonators does not affect the electromagnetic mode profile andthe current/charge distributions of each one of the resonators.Therefore, when these resonators have a high (unloaded and unperturbed)Q, their (unloaded and unperturbed) Q may be preserved in the presenceof the wireless coupling. (Note that the loaded Q of a resonator may bereduced in the presence of wireless coupling to another resonator, butwe may be interested in preserving the unloaded Q, which relates only toloss mechanisms and not to coupling/loading mechanisms.)

Consider a matching topology such as is shown in FIG. 28( b). Thecapacitors shown in FIG. 28( b) may represent capacitor circuits ornetworks. The capacitors shown may be used to form the resonator 102 andto adjust the frequency and/or impedance of the source and deviceresonators. This resonator 102 may be directly coupled to an impedance,Z₀, using the ports labeled “terminal connections” 2808. FIG. 28( c)shows a generalized directly coupled matching topology, where theimpedance-matching circuit 2602 includes or consists of parts A, B andC. Here, circuit elements in A, B and C may be considered part of theresonator 102 as well as part of the impedance matching 2402 (andfrequency tuning) topology. B and C may be the parts of the matchingcircuit 2402 that connect the impedance Z₀ 2804 (or the networkterminals) to the rest of the circuit (A and the inductive element) viaa single wire connection each. Note that B and C could be empty(short-circuits). If we disconnect or open circuit parts B and C (namelythose single wire connections), then, the combination of A and theinductive element (R,L) may form the resonator.

The high-Q resonator electromagnetic mode may be such that the profileof the voltage distribution along the inductive element has nodes,namely positions where the voltage is zero. One node may beapproximately at the center of the length of the inductive element, suchas the center of the conductor used to form the inductive element, (withor without magnetic materials) and at least one other node may be withinA. The voltage distribution may be approximately anti-symmetric alongthe inductive element with respect to its voltage node. A high Q may bemaintained by designing the matching topology (A, B, C) and/or theterminal voltages (V1, V2) so that this high-Q resonator electromagneticmode distribution may be approximately preserved on the inductiveelement. This high-Q resonator electromagnetic mode distribution may beapproximately preserved on the inductive element by preserving thevoltage node (approximately at the center) of the inductive element.Examples that achieve these design goals are provided herein.

A, B, and C may be arbitrary (namely not having any special symmetry),and V1 and V2 may be chosen so that the voltage across the inductiveelement is symmetric (voltage node at the center inductive). Theseresults may be achieved using simple matching circuits but potentiallycomplicated terminal voltages, because a topology-dependent common-modesignal (V1+V2)/2 may be required on both terminals.

Consider an ‘axis’ that connects all the voltage nodes of the resonator,where again one node is approximately at the center of the length of theinductive element and the others within A. (Note that the ‘axis’ isreally a set of points (the voltage nodes) within the electric-circuittopology and may not necessarily correspond to a linear axis of theactual physical structure. The ‘axis’ may align with a physical axis incases where the physical structure has symmetry.) Two points of theresonator are electrically symmetric with respect to the ‘axis’, if theimpedances seen between each of the two points and a point on the‘axis’, namely a voltage-node point of the resonator, are the same.

B and C may be the same (C=B), and the two terminals may be connected toany two points of the resonator (A+(R,L)) that are electricallysymmetric with respect to the ‘axis’ defined above and driven withopposite voltages (V2=−V1) as shown in FIG. 28( d). The two electricallysymmetric points of the resonator 102 may be two electrically symmetricpoints on the inductor loop. The two electrically symmetric points ofthe resonator may be two electrically symmetric points inside A. If thetwo electrically symmetric points, (to which each of the equal parts Band C is connected), are inside A, A may need to be designed so thatthese electrically-symmetric points are accessible as connection pointswithin the circuit. This topology may be referred to as a ‘balanceddrive’ topology. These balanced-drive examples may have the advantagethat any common-mode signal that may be present on the ground line, dueto perturbations at the external circuitry or the power network, forexample, may be automatically rejected (and may not reach theresonator). In some balanced-drive examples, this topology may requiremore components than other topologies.

In other examples, C may be chosen to be a short-circuit and thecorresponding terminal to be connected to ground (V=0) and to any pointon the electric-symmetry (zero-voltage) ‘axis’ of the resonator, and Bto be connected to any other point of the resonator not on theelectric-symmetry ‘axis’, as shown in FIG. 28( e). The ground-connectedpoint on the electric-symmetry ‘axis’ may be the voltage node on theinductive element, approximately at the center of its conductor length.The ground-connected point on the electric-symmetry ‘axis’ may be insidethe circuit A. Where the ground-connected point on the electric-symmetry‘axis’ is inside A, A may need to be designed to include one such pointon the electrical-symmetric ‘axis’ that is electrically accessible,namely where connection is possible.

This topology may be referred to as an ‘unbalanced drive’ topology. Theapproximately anti-symmetric voltage distribution of the electromagneticmode along the inductive element may be approximately preserved, eventhough the resonator may not be driven exactly symmetrically. The reasonis that the high Q and the large associated R-vs.-Z₀ mismatchnecessitate that a small current may run through B and ground, comparedto the much larger current that may flow inside the resonator,(A+(R,L)). In this scenario, the perturbation on the resonator mode maybe weak and the location of the voltage node may stay at approximatelythe center location of the inductive element. These unbalanced-driveexamples may have the advantage that they may be achieved using simplematching circuits and that there is no restriction on the drivingvoltage at the V1 terminal. In some unbalanced-drive examples,additional designs may be required to reduce common-mode signals thatmay appear at the ground terminal.

The directly-coupled impedance-matching circuit, generally including orconsisting of parts A, B and C, as shown in FIG. 28( c), may be designedso that the wires and components of the circuit do not perturb theelectric and magnetic field profiles of the electromagnetic mode of theinductive element and/or the resonator and thus preserve the highresonator Q. The wires and metallic components of the circuit may beoriented to be perpendicular to the electric field lines of theelectromagnetic mode. The wires and components of the circuit may beplaced in regions where the electric and magnetic field of theelectromagnetic mode are weak.

Topologies for Alleviating Low-Series-Loss and High-Current-RatingRequirements on Elements

If the matching circuit used to match a small resistance, R, of alow-loss inductive element to a larger characteristic impedance, Z₀, ofan external circuit may be considered lossless, then I_(Z) _(o)²Z_(o)=I_(R) ²R

I_(Z) _(o) /I_(R)=√{square root over (R/Z_(o))} and the current flowingthrough the terminals is much smaller than the current flowing throughthe inductive element. Therefore, elements connected immediately inseries with the terminals (such as in directly-coupled B, C (FIG. 28(c))) may not carry high currents. Then, even if the matching circuit haslossy elements, the resistive loss present in the elements in serieswith the terminals may not result in a significant reduction in thehigh-Q of the resonator. That is, resistive loss in those serieselements may not significantly reduce the efficiency of powertransmission from Z₀ to the inductive element or vice versa. Therefore,strict requirements for low-series-loss and/or high current-ratings maynot be necessary for these components. In general, such reducedrequirements may lead to a wider selection of components that may bedesigned into the high-Q and/or high-power impedance matching andresonator topologies. These reduced requirements may be especiallyhelpful in expanding the variety of variable and/or high voltage and/orlow-parallel-loss components that may be used in these high-Q and/orhigh-power impedance-matching circuits.

Topologies for Alleviating Low-Parallel-Loss and High-Voltage-RatingRequirements on Elements

If, as above, the matching circuit used to match a small resistance, R,of a low-loss inductive element to a larger characteristic impedance,Z₀, of an external circuit is lossless, then using the previousanalysis,|V _(Z) _(o) /V _(load) |=|I _(Z) _(o) /I _(R)(R+jX)|≈√{square root over(R/Z _(o))}·Z _(o) /X=√{square root over (Z_(o) /R)}/(X/R),and, for a low-loss (high-X/R) inductive element, the voltage across theterminals may be typically much smaller than the voltage across theinductive element. Therefore, elements connected immediately in parallelto the terminals may not need to withstand high voltages. Then, even ifthe matching circuit has lossy elements, the resistive loss present inthe elements in parallel with the terminals may not result in asignificant reduction in the high-Q of the resonator. That is, resistiveloss in those parallel elements may not significantly reduce theefficiency of power transmission from Z₀ to the inductive element orvice versa. Therefore, strict requirements for low-parallel-loss and/orhigh voltage-ratings may not be necessary for these components. Ingeneral, such reduced requirements may lead to a wider selection ofcomponents that may be designed into the high-Q and/or high-powerimpedance matching and resonator topologies. These reduced requirementsmay be especially helpful in expanding the variety of variable and/orhigh current and/or low-series-loss components that may be used in thesehigh-Q and/or high-power impedance-matching and resonator circuits.

Note that the design principles above may reduce currents and voltageson various elements differently, as they variously suggest the use ofnetworks in series with Z₀ (such as directly-coupled B, C) or the use ofnetworks in parallel with Z₀. The preferred topology for a givenapplication may depend on the availability oflow-series-loss/high-current-rating orlow-parallel-loss/high-voltage-rating elements.

Combinations of Fixed and Variable Elements for Achieving FineTunability and Alleviating High-Rating Requirements on Variable Elements

Circuit Topologies

Variable circuit elements with satisfactory low-loss and high-voltage orcurrent ratings may be difficult or expensive to obtain. In thisdisclosure, we describe impedance-matching topologies that mayincorporate combinations of fixed and variable elements, such that largevoltages or currents may be assigned to fixed elements in the circuit,which may be more likely to have adequate voltage and current ratings,and alleviating the voltage and current rating requirements on thevariable elements in the circuit.

Variable circuit elements may have tuning ranges larger than thoserequired by a given impedance-matching application and, in those cases,fine tuning resolution may be difficult to obtain using only suchlarge-range elements. In this disclosure, we describe impedance-matchingtopologies that incorporate combinations of both fixed and variableelements, such that finer tuning resolution may be accomplished with thesame variable elements.

Therefore, topologies using combinations of both fixed and variableelements may bring two kinds of advantages simultaneously: reducedvoltage across, or current through, sensitive tuning components in thecircuit and finer tuning resolution. Note that the maximum achievabletuning range may be related to the maximum reduction in voltage across,or current through, the tunable components in the circuit designs.

Element Topologies

A single variable circuit-element (as opposed to the network of elementsdiscussed above) may be implemented by a topology using a combination offixed and variable components, connected in series or in parallel, toachieve a reduction in the rating requirements of the variablecomponents and a finer tuning resolution. This can be demonstratedmathematically by the fact that:If x _(|total|) =x _(|fixed|) +x _(|variable|),then Δx _(|total|) /x _(|total|) =Δx _(|variable|)/(x _(|fixed|) +x_(|variable|))and X _(varable) /X _(total) =X _(variable)/(X _(fixed) +X _(variable)),where x_(|subscript|) is any element value (e.g. capacitance,inductance), X is voltage or current, and the “+sign” denotes theappropriate (series-addition or parallel-addition) combination ofelements. Note that the subscript format for x_(|subscript|), is chosento easily distinguish it from the radius of the area enclosed by acircular inductive element (e.g. x, x₁, etc.).

Furthermore, this principle may be used to implement a variable electricelement of a certain type (e.g. a capacitance or inductance) by using avariable element of a different type, if the latter is combinedappropriately with other fixed elements.

In conclusion, one may apply a topology optimization algorithm thatdecides on the required number, placement, type and values of fixed andvariable elements with the required tunable range as an optimizationconstraint and the minimization of the currents and/or voltages on thevariable elements as the optimization objective.

EXAMPLES

In the following schematics, we show different specific topologyimplementations for impedance matching to and resonator designs for alow-loss inductive element. In addition, we indicate for each topology:which of the principles described above are used, the equations givingthe values of the variable elements that may be used to achieve thematching, and the range of the complex impedances that may be matched(using both inequalities and a Smith-chart description). For theseexamples, we assume that Z₀ is real, but an extension to acharacteristic impedance with a non-zero imaginary part isstraightforward, as it implies only a small adjustment in the requiredvalues of the components of the matching network. We will use theconvention that the subscript, n, on a quantity implies normalization to(division by) Z₀.

FIG. 29 shows two examples of a transformer-coupled impedance-matchingcircuit, where the two tunable elements are a capacitor and the mutualinductance between two inductive elements. If we define respectivelyX₂=ωL₂ for FIG. 29( a) and X₂=ωL₂−1/ωC₂ for FIG. 29( b), and X≡ωL thenthe required values of the tunable elements are:

${\omega\; C_{1}} = \frac{1}{X + {RX}_{2n}}$${\omega\; M} = {\sqrt{Z_{o}{R\left( {1 + X_{2n}^{2}} \right)}}.}$For the topology of FIG. 29( b), an especially straightforward designmay be to choose X₂=0. In that case, these topologies may match theimpedances satisfying the inequalities:R _(n)>0,X _(n)>0,which are shown by the area enclosed by the bold lines on the Smithchart of FIG. 29( c).

Given a well pre-chosen fixed M, one can also use the above matchingtopologies with a tunable C₂ instead.

FIG. 30 shows six examples (a)-(f) of directly-coupledimpedance-matching circuits, where the two tunable elements arecapacitors, and six examples (h)-(m) of directly-coupledimpedance-matching circuits, where the two tunable elements are onecapacitor and one inductor. For the topologies of FIGS. 30(a),(b),(c),(h),(i),(j), a common-mode signal may be required at the twoterminals to preserve the voltage node of the resonator at the center ofthe inductive element and thus the high Q. Note that these examples maybe described as implementations of the general topology shown in FIG.28( c). For the symmetric topologies of FIGS. 30(d),(e),(f),(k),(l),(m), the two terminals may need to be drivenanti-symmetrically (balanced drive) to preserve the voltage node of theresonator at the center of the inductive element and thus the high Q.Note that these examples may be described as implementations of thegeneral topology shown in FIG. 28( d). It will be appreciated that anetwork of capacitors, as used herein, may in general refer to anycircuit topology including one or more capacitors, including withoutlimitation any of the circuits specifically disclosed herein usingcapacitors, or any other equivalent or different circuit structure(s),unless another meaning is explicitly provided or otherwise clear fromthe context.

Let us define respectively Z=R+jωL for FIGS. 30( a),(d),(h),(k),Z=R+jωL+1/jωC₃ for FIGS. 30( b),(e),(i),(l), and Z=(R+jωL)∥(1/jωC₃) forFIGS. 30( c),(f),(j),(m), where the symbol “∥” means “the parallelcombination of”, and then R≡Re{Z}, X≡Im{Z}. Then, for FIGS. 30( a)-(f)the required values of the tunable elements may be given by:

${{\omega\; C_{1}} = \frac{X - \sqrt{{X^{2}R_{n}} - {R^{2}\left( {1 - R_{n}} \right)}}}{X^{2} + R^{2}}},{{\omega\; C_{2}} = \frac{R_{n}\omega\; C_{1}}{{1 - {X\;\omega\; C_{1}} - R_{n}}\;}},$and these topologies can match the impedances satisfying theinequalities:R _(n)≦1,X _(n)≧√{square root over (R_(n)(1−R _(n)))}which are shown by the area enclosed by the bold lines on the Smithchart of FIG. 30( g). For FIGS. 30( h)-(m) the required values of thetunable elements may be given by:

${{\omega\; C_{1}} = \frac{X + \sqrt{{X^{2}R_{n}} - {R^{2}\left( {1 - R_{n}} \right)}}}{X^{2} + R^{2}}},{{\omega\; L_{2}} = {- {\frac{1 - {X\;\omega\; C_{1}} - R_{n}}{R_{n}\omega\; C_{1}}.}}}$

FIG. 31 shows three examples (a)-(c) of directly-coupledimpedance-matching circuits, where the two tunable elements arecapacitors, and three examples (e)-(g) of directly-coupledimpedance-matching circuits, where the two tunable elements are onecapacitor and one inductor. For the topologies of FIGS. 31(a),(b),(c),(e),(f),(g), the ground terminal is connected between twoequal-value capacitors, 2C₁, (namely on the axis of symmetry of the mainresonator) to preserve the voltage node of the resonator at the centerof the inductive element and thus the high Q. Note that these examplesmay be described as implementations of the general topology shown inFIG. 28( e).

Let us define respectively Z=R+jωL for FIGS. 31( a),(e), Z=R+jωL+1/jωC₃for FIGS. 31( b),(f), and Z=(R+jωL)∥(1/jωC₃) for FIG. 31( c),(g), andthen R≡Re{Z}, X≡Im{Z}. Then, for FIGS. 31( a)-(c) the required values ofthe tunable elements may be given by:

${{\omega\; C_{1}} = \frac{X - {\frac{1}{2}\sqrt{{X^{2}R_{n}} - {R^{2}\left( {4 - R_{n}} \right)}}}}{X^{2} + R^{2\;}}},{{\omega\; C_{2}} = \frac{R_{n}\omega\; C_{1}}{1 - {X\;\omega\; C_{1}} - \frac{R_{n}}{2}}},$and these topologies can match the impedances satisfying theinequalities:

${R_{n} \leq 1},{X_{n} \geq {\sqrt{\frac{R_{n}}{1 - R_{n}}}\left( {2 - R_{n}} \right)}}$which are shown by the area enclosed by the bold lines on the Smithchart of FIG. 31( d). For FIGS. 31( e)-(g) the required values of thetunable elements may be given by:

${{\omega\; C_{1}} = \frac{X + {\frac{1}{2}\sqrt{{X^{2}R_{n}} - {R^{2}\left( {4 - R_{n}} \right)}}}}{X^{2} + R^{2}}},{{\omega\; L_{2}} = {- {\frac{1 - {X\;\omega\; C_{1}} - \frac{R_{n}}{2}}{R_{n}\omega\; C_{1}}.}}}$

FIG. 32 shows three examples (a)-(c) of directly-coupledimpedance-matching circuits, where the two tunable elements arecapacitors, and three examples (e)-(g) of directly-coupledimpedance-matching circuits, where the two tunable elements are onecapacitor and one inductor. For the topologies of FIGS. 32(a),(b),(c),(e),(f),(g), the ground terminal may be connected at thecenter of the inductive element to preserve the voltage node of theresonator at that point and thus the high Q. Note that these example maybe described as implementations of the general topology shown in FIG.28( e).

Let us define respectively Z=R+jωL for FIG. 32( a), Z=R+jωL+1/jωC₃ forFIG. 32( b), and Z=(R+jωL)∥(1/jωC₃) for FIG. 32( c), and then R≡Re{Z},X≡Im{Z}. Then, for FIGS. 32( a)-(c) the required values of the tunableelements may be given by:

${{\omega\; C_{1}} = \frac{X - \sqrt{\frac{{X^{2}R_{n}} - {2{R^{2}\left( {2 - R_{n}} \right)}}}{4 - R_{n}}}}{X^{2} + R^{2}}},{{\omega\; C_{2}} = \frac{R_{n}\omega\; C_{1}}{1 - {X\;\omega\; C_{1}} - \frac{R_{n}}{2} + \frac{R_{n}X\;\omega\; C_{1}}{2\left( {1 + k} \right)}}},$where k is defined by M′=−kL′, where L′ is the inductance of each halfof the inductor loop and M′ is the mutual inductance between the twohalves, and these topologies can match the impedances satisfying theinequalities:R _(n)≦2,X _(n)≧√{square root over (2 R _(n)(2−R _(n)))}which are shown by the area enclosed by the bold lines on the Smithchart of FIG. 32( d). For FIGS. 32( e)-(g) the required values of thetunable elements may be given by:

${{\omega\; C_{1}} = \frac{X + \sqrt{\frac{{X^{2}R_{n}} - {2{R^{2}\left( {2 - R_{n}} \right)}}}{4 - R_{n}}}}{X^{2} + R^{2}}},$

In the circuits of FIGS. 30, 31, 32, the capacitor, C₂, or the inductor,L₂, is (or the two capacitors, 2C₂, or the two inductors, L₂/2, are) inseries with the terminals and may not need to have very low series-lossor withstand a large current.

FIG. 33 shows six examples (a)-(f) of directly-coupledimpedance-matching circuits, where the two tunable elements arecapacitors, and six examples (h)-(m) of directly-coupledimpedance-matching circuits, where the two tunable elements are onecapacitor and one inductor. For the topologies of FIGS. 33(a),(b),(c),(h),(i),(j), a common-mode signal may be required at the twoterminals to preserve the voltage node of the resonator at the center ofthe inductive element and thus the high Q. Note that these examples maybe described as implementations of the general topology shown in FIG.28( c), where B and C are short-circuits and A is not balanced. For thesymmetric topologies of FIGS. 33( d),(e),(f),(k),(l),(m), the twoterminals may need to be driven anti-symmetrically (balanced drive) topreserve the voltage node of the resonator at the center of theinductive element and thus the high Q. Note that these examples may bedescribed as implementations of the general topology shown in FIG. 28(d), where B and C are short-circuits and A is balanced.

Let us define respectively Z=R+jωL for FIGS. 33( a),(d),(h),(k),Z=R+jωL+1/jωC₃ for FIGS. 33( b),(e),(i),(l), and Z=(R+jωL)∥(1/jωC₃) forFIGS. 33( c),(f),(j),(m), and then R≡Re{Z}, X≡Im{Z}. Then, for FIGS. 33(a)-(f) the required values of the tunable elements may be given by:

${{\omega\; C_{1}} = \frac{1}{X - {Z_{o}\sqrt{R_{n}\left( {1 - R_{n}} \right)}}}},{{\omega\; C_{2}} = {\frac{1}{Z_{o}}\sqrt{\frac{1}{R_{n}} - 1}}},$and these topologies can match the impedances satisfying theinequalities:R _(n)≦1,X _(n)≧√{square root over (R_(n)(1−R _(n)))}which are shown by the area enclosed by the bold lines on the Smithchart of FIG. 33( g). For FIGS. 35( h)-(m) the required values of thetunable elements may be given by:

${{\omega\; C_{1}} = \frac{1}{X + {Z_{o}\sqrt{R_{n}\left( {1 - R_{n}} \right)}}}},{{\omega\; L_{2}} = {\frac{Z_{o}}{\sqrt{\frac{1}{R_{n}} - 1}}.}}$

FIG. 34 shows three examples (a)-(c) of directly-coupledimpedance-matching circuits, where the two tunable elements arecapacitors, and three examples (e)-(g) of directly-coupledimpedance-matching circuits, where the two tunable elements are onecapacitor and one inductor. For the topologies of FIGS. 34(a),(b),(c),(e),(f),(g), the ground terminal is connected between twoequal-value capacitors, 2C₂, (namely on the axis of symmetry of the mainresonator) to preserve the voltage node of the resonator at the centerof the inductive element and thus the high Q. Note that these examplesmay be described as implementations of the general topology shown inFIG. 28( e).

Let us define respectively Z=R+jωL for FIG. 34( a),(e), Z=R+jωL+1/jωC₃for FIG. 34( b),(f), and Z=(R+jωL) 11 (1/jωC₃) for FIG. 34( c),(g), andthen R≡Re{Z}, X≡Im{Z}. Then, for FIGS. 34( a)-(c) the required values ofthe tunable elements may be given by:

${{\omega\; C_{1}} = \frac{1}{X - {Z_{o}\sqrt{\frac{1 - R_{n}}{R_{n}}}\left( {2 - R_{n}} \right)}}},{{\omega\; C_{2}} = {\frac{1}{2Z_{o}}\sqrt{\frac{1}{R_{n}} - 1}}},$and these topologies can match the impedances satisfying theinequalities:

${R_{n} \leq 1},{X_{n} \geq {\sqrt{\frac{R_{n}}{1 - R_{n}}}\left( {2 - R_{n}} \right)}}$which are shown by the area enclosed by the bold lines on the Smithchart of FIG. 34( d). For FIGS. 34( e)-(g) the required values of thetunable elements may be given by:

${{\omega\; C_{1}} = \frac{1}{X + {Z_{o}\;\sqrt{\frac{1 - R_{n}}{R_{n}}}\left( {2 - R_{n}} \right)}}},{{\omega\; L_{2}} = {\frac{2Z_{o}}{\sqrt{\frac{1}{R_{n}} - 1}}.}}$

FIG. 35 shows three examples of directly-coupled impedance-matchingcircuits, where the two tunable elements are capacitors. For thetopologies of FIG. 35, the ground terminal may be connected at thecenter of the inductive element to preserve the voltage node of theresonator at that point and thus the high Q. Note that these examplesmay be described as implementations of the general topology shown inFIG. 28( e).

Let us define respectively Z=R+jωL for FIG. 35( a), Z=R+jωL+1/jωC₃ forFIG. 35( b), and Z=(R+jωL)∥(1/jωC₃) for FIG. 35( c), and then R≡Re{Z},X≡Im{Z}. Then, the required values of the tunable elements may be givenby:

${{\omega\; C_{1}} = \frac{2}{{X\left( {1 + a} \right)} - \sqrt{Z_{o}{R\left( {4 - R_{n}} \right)}\left( {1 + a^{2}} \right)}}},{{\omega\; C_{2}} = \frac{2}{{X\left( {1 + a} \right)} + \sqrt{Z_{o}{R\left( {4 - R_{n}} \right)}\left( {1 + a^{2}} \right)}}},{where}$$a = {\frac{R}{{2Z_{o}} - R} \cdot \frac{k}{1 + k}}$and k is defined by M′=−kL′, where L′ is the inductance of each half ofthe inductive element and M′ is the mutual inductance between the twohalves. These topologies can match the impedances satisfying theinequalities:

${{{{R_{n} \leq 2}\&}\mspace{14mu}\frac{2}{\gamma}} \leq R_{n} \leq 4},{X_{n} \geq \sqrt{\frac{{R_{n}\left( {4 - R_{n}} \right)}\left( {2 - R_{n}} \right)}{2 - {\gamma\; R_{n}}}}},{where}$$\gamma = {\frac{1 - {6k} + k^{2}}{1 + {2k} + k^{2}} \leq 1}$which are shown by the area enclosed by the bold lines on the threeSmith charts shown in FIG. 35( d) for k=0, FIG. 35( e) for k=0.05, andFIG. 35( f) for k=1. Note that for 0<k<1 there are two disconnectedregions of the Smith chart that this topology can match.

In the circuits of FIGS. 33, 34, 35, the capacitor, C₂, or the inductor,L₂, is (or one of the two capacitors, 2C₂, or one of the two inductors,2L₂, are) in parallel with the terminals and thus may not need to have ahigh voltage-rating. In the case of two capacitors, ²C₂, or twoinductors, 2L₂, both may not need to have a high voltage-rating, sinceapproximately the same current flows through them and thus theyexperience approximately the same voltage across them.

For the topologies of FIGS. 30-35, where a capacitor, C₃, is used, theuse of the capacitor, C₃, may lead to finer tuning of the frequency andthe impedance. For the topologies of FIGS. 30-35, the use of the fixedcapacitor, C₃, in series with the inductive element may ensure that alarge percentage of the high inductive-element voltage will be acrossthis fixed capacitor, C₃, thus potentially alleviating the voltagerating requirements for the other elements of the impedance matchingcircuit, some of which may be variable. Whether or not such topologiesare preferred depends on the availability, cost and specifications ofappropriate fixed and tunable components.

In all the above examples, a pair of equal-value variable capacitorswithout a common terminal may be implemented using ganged-typecapacitors or groups or arrays of varactors or diodes biased andcontrolled to tune their values as an ensemble. A pair of equal-valuevariable capacitors with one common terminal can be implemented using atunable butterfly-type capacitor or any other tunable or variablecapacitor or group or array of varactors or diodes biased and controlledto tune their capacitance values as an ensemble.

Another criterion which may be considered upon the choice of theimpedance matching network is the response of the network to differentfrequencies than the desired operating frequency. The signals generatedin the external circuit, to which the inductive element is coupled, maynot be monochromatic at the desired frequency but periodic with thedesired frequency, as for example the driving signal of a switchingamplifier or the reflected signal of a switching rectifier. In some suchcases, it may be desirable to suppress the amount of higher-orderharmonics that enter the inductive element (for example, to reduceradiation of these harmonics from this element). Then the choice ofimpedance matching network may be one that sufficiently suppresses theamount of such harmonics that enters the inductive element.

The impedance matching network may be such that the impedance seen bythe external circuit at frequencies higher than the fundamental harmonicis high, when the external periodic signal is a signal that can beconsidered to behave as a voltage-source signal (such as the drivingsignal of a class-D amplifier with a series resonant load), so thatlittle current flows through the inductive element at higherfrequencies. Among the topologies of FIGS. 30-35, those which use aninductor, L₂, may then be preferable, as this inductor presents a highimpedance at high frequencies.

The impedance matching network may be such that the impedance seen bythe external circuit at frequencies higher than the fundamental harmonicis low, when the external periodic signal is a signal that can beconsidered to behave as a current-source signal, so that little voltageis induced across the inductive element at higher frequencies. Among thetopologies of FIGS. 30-35, those which use a capacitor, C₂, are thenpreferable, as this capacitor presents a low impedance at highfrequencies.

FIG. 36 shows four examples of a variable capacitance, using networks ofone variable capacitor and the rest fixed capacitors. Using thesenetwork topologies, fine tunability of the total capacitance value maybe achieved. Furthermore, the topologies of FIGS. 36( a),(c),(d), may beused to reduce the voltage across the variable capacitor, since most ofthe voltage may be assigned across the fixed capacitors.

FIG. 37 shows two examples of a variable capacitance, using networks ofone variable inductor and fixed capacitors. In particular, thesenetworks may provide implementations for a variable reactance, and, atthe frequency of interest, values for the variable inductor may be usedsuch that each network corresponds to a net negative variable reactance,which may be effectively a variable capacitance.

Tunable elements such as tunable capacitors and tunable inductors may bemechanically-tunable, electrically-tunable, thermally-tunable and thelike. The tunable elements may be variable capacitors or inductors,varactors, diodes, Schottky diodes, reverse-biased PN diodes, varactorarrays, diode arrays, Schottky diode arrays and the like. The diodes maybe Si diodes, GaN diodes, SiC diodes, and the like. GaN and SiC diodesmay be particularly attractive for high power applications. The tunableelements may be electrically switched capacitor banks,electrically-switched mechanically-tunable capacitor banks,electrically-switched varactor-array banks, electrically-switchedtransformer-coupled inductor banks, and the like. The tunable elementsmay be combinations of the elements listed above.

As described above, the efficiency of the power transmission betweencoupled high-Q magnetic resonators may be impacted by how closelymatched the resonators are in resonant frequency and how well theirimpedances are matched to the power supplies and power consumers in thesystem. Because a variety of external factors including the relativeposition of extraneous objects or other resonators in the system, or thechanging of those relative positions, may alter the resonant frequencyand/or input impedance of a high-Q magnetic resonator, tunable impedancenetworks may be required to maintain sufficient levels of powertransmission in various environments or operating scenarios.

The capacitance values of the capacitors shown may be adjusted to adjustthe resonant frequency and/or the impedance of the magnetic resonator.The capacitors may be adjusted electrically, mechanically, thermally, orby any other known methods. They may be adjusted manually orautomatically, such as in response to a feedback signal. They may beadjusted to achieve certain power transmission efficiencies or otheroperating characteristics between the power supply and the powerconsumer.

The inductance values of the inductors and inductive elements in theresonator may be adjusted to adjust the frequency and/or impedance ofthe magnetic resonator. The inductance may be adjusted using coupledcircuits that include adjustable components such as tunable capacitors,inductors and switches. The inductance may be adjusted using transformercoupled tuning circuits. The inductance may be adjusted by switching inand out different sections of conductor in the inductive elements and/orusing ferro-magnetic tuning and/or mu-tuning, and the like.

The resonant frequency of the resonators may be adjusted to or may beallowed to change to lower or higher frequencies. The input impedance ofthe resonator may be adjusted to or may be allowed to change to lower orhigher impedance values. The amount of power delivered by the sourceand/or received by the devices may be adjusted to or may be allowed tochange to lower or higher levels of power. The amount of power deliveredto the source and/or received by the devices from the device resonatormay be adjusted to or may be allowed to change to lower or higher levelsof power. The resonator input impedances, resonant frequencies, andpower levels may be adjusted depending on the power consumer orconsumers in the system and depending on the objects or materials in thevicinity of the resonators. The resonator input impedances, frequencies,and power levels may be adjusted manually or automatically, and may beadjusted in response to feedback or control signals or algorithms.

Circuit elements may be connected directly to the resonator, that is, byphysical electrical contact, for example to the ends of the conductorthat forms the inductive element and/or the terminal connectors. Thecircuit elements may be soldered to, welded to, crimped to, glued to,pinched to, or closely position to the conductor or attached using avariety of electrical components, connectors or connection techniques.The power supplies and the power consumers may be connected to magneticresonators directly or indirectly or inductively. Electrical signals maybe supplied to, or taken from, the resonators through the terminalconnections.

It is to be understood by one of ordinary skill in the art that in realimplementations of the principles described herein, there may be anassociated tolerance, or acceptable variation, to the values of realcomponents (capacitors, inductors, resistors and the like) from thevalues calculated via the herein stated equations, to the values of realsignals (voltages, currents and the like) from the values suggested bysymmetry or anti-symmetry or otherwise, and to the values of realgeometric locations of points (such as the point of connection of theground terminal close to the center of the inductive element or the‘axis’ points and the like) from the locations suggested by symmetry orotherwise.

EXAMPLES System Block Diagrams

We disclose examples of high-Q resonators for wireless powertransmission systems that may wirelessly power or charge devices atmid-range distances. High-Q resonator wireless power transmissionsystems also may wirelessly power or charge devices with magneticresonators that are different in size, shape, composition, arrangement,and the like, from any source resonators in the system.

FIG. 1( a)(b) shows high level diagrams of two exemplary two-resonatorsystems. These exemplary systems each have a single source resonator1025 or 104S and a single device resonator 102D or 104D. FIG. 38 shows ahigh level block diagram of a system with a few more featureshighlighted. The wirelessly powered or charged device 2310 may includeor consist of a device resonator 102D, device power and controlcircuitry 2304, and the like, along with the device 2308 or devices, towhich either DC or AC or both AC and DC power is transferred. The energyor power source for a system may include the source power and controlcircuitry 2302, a source resonator 102S, and the like. The device 2308or devices that receive power from the device resonator 102D and powerand control circuitry 2304 may be any kind of device 2308 or devices asdescribed previously. The device resonator 102D and circuitry 2304delivers power to the device/devices 2308 that may be used to rechargethe battery of the device/devices, power the device/devices directly, orboth when in the vicinity of the source resonator 102S.

The source and device resonators may be separated by many meters or theymay be very close to each other or they may be separated by any distancein between. The source and device resonators may be offset from eachother laterally or axially. The source and device resonators may bedirectly aligned (no lateral offset), or they may be offset by meters,or anything in between. The source and device resonators may be orientedso that the surface areas enclosed by their inductive elements areapproximately parallel to each other. The source and device resonatorsmay be oriented so that the surface areas enclosed by their inductiveelements are approximately perpendicular to each other, or they may beoriented for any relative angle (0 to 360 degrees) between them.

The source and device resonators may be free standing or they may beenclosed in an enclosure, container, sleeve or housing. These variousenclosures may be composed of almost any kind of material. Low losstangent materials such as Teflon, REXOLITE, styrene, and the like may bepreferable for some applications. The source and device resonators maybe integrated in the power supplies and power consumers. For example,the source and device resonators may be integrated into keyboards,computer mice, displays, cell phones, etc. so that they are not visibleoutside these devices. The source and device resonators may be separatefrom the power supplies and power consumers in the system and may beconnected by a standard or custom wires, cables, connectors or plugs.

The source 102S may be powered from a number of DC or AC voltage,current or power sources including a USB port of a computer. The source1025 may be powered from the electric grid, from a wall plug, from abattery, from a power supply, from an engine, from a solar cell, from agenerator, from another source resonator, and the like. The source powerand control circuitry 2302 may include circuits and components toisolate the source electronics from the power source, so that anyreflected power or signals are not coupled out through the source inputterminals. The source power and control circuits 2302 may include powerfactor correction circuits and may be configured to monitor power usagefor monitoring accounting, billing, control, and like functionalities.

The system may be operated bi-directionally. That is, energy or powerthat is generated or stored in a device resonator may be fed back to apower source including the electric grid, a battery, any kind of energystorage unit, and the like. The source power and control circuits mayinclude power factor correction circuits and may be configured tomonitor power usage for monitoring accounting, billing, control, andlike functionalities for bi-directional energy flow. Wireless energytransfer systems may enable or promote vehicle-to-grid (V2G)applications.

The source and the device may have tuning capabilities that allowadjustment of operating points to compensate for changing environmentalconditions, perturbations, and loading conditions that can affect theoperation of the source and device resonators and the efficiency of theenergy exchange. The tuning capability may also be used to multiplexpower delivery to multiple devices, from multiple sources, to multiplesystems, to multiple repeaters or relays, and the like. The tuningcapability may be manually controlled, or automatically controlled andmay be performed continuously, periodically, intermittently or atscheduled times or intervals.

The device resonator and the device power and control circuitry may beintegrated into any portion of the device, such as a batterycompartment, or a device cover or sleeve, or on a mother board, forexample, and may be integrated alongside standard rechargeable batteriesor other energy storage units. The device resonator may include a devicefield reshaper which may shield any combination of the device resonatorelements and the device power and control electronics from theelectromagnetic fields used for the power transfer and which may deflectthe resonator fields away from the lossy device resonator elements aswell as the device power and control electronics. A magnetic materialand/or high-conductivity field reshaper may be used to increase theperturbed quality factor Q of the resonator and increase the perturbedcoupling factor of the source and device resonators.

The source resonator and the source power and control circuitry may beintegrated into any type of furniture, structure, mat, rug, pictureframe (including digital picture frames, electronic frames), plug-inmodules, electronic devices, vehicles, and the like. The sourceresonator may include a source field reshaper which may shield anycombination of the source resonator elements and the source power andcontrol electronics from the electromagnetic fields used for the powertransfer and which may deflect the resonator fields away from the lossysource resonator elements as well as the source power and controlelectronics. A magnetic material and/or high-conductivity field reshapermay be used to increase the perturbed quality factor Q of the resonatorand increase the perturbed coupling factor of the source and deviceresonators.

A block diagram of the subsystems in an example of a wirelessly powereddevice is shown in FIG. 39. The power and control circuitry may bedesigned to transform the alternating current power from the deviceresonator 102D and convert it to stable direct current power suitablefor powering or charging a device. The power and control circuitry maybe designed to transform an alternating current power at one frequencyfrom the device resonator to alternating current power at a differentfrequency suitable for powering or charging a device. The power andcontrol circuitry may include or consist of impedance matching circuitry2402D, rectification circuitry 2404, voltage limiting circuitry (notshown), current limiting circuitry (not shown), AC-to-DC converter 2408circuitry, DC-to-DC converter 2408 circuitry, DC-to-AC converter 2408circuitry, AC-to-AC converter 2408 circuitry, battery charge controlcircuitry (not shown), and the like.

The impedance-matching 2402D network may be designed to maximize thepower delivered between the device resonator 102D and the device powerand control circuitry 2304 at the desired frequency. The impedancematching elements may be chosen and connected such that the high-Q ofthe resonators is preserved. Depending on the operating conditions, theimpedance matching circuitry 2402D may be varied or tuned to control thepower delivered from the source to the device, from the source to thedevice resonator, between the device resonator and the device power andcontrol circuitry, and the like. The power, current and voltage signalsmay be monitored at any point in the device circuitry and feedbackalgorithms circuits, and techniques, may be used to control componentsto achieve desired signal levels and system operation. The feedbackalgorithms may be implemented using analog or digital circuit techniquesand the circuits may include a microprocessor, a digital signalprocessor, a field programmable gate array processor and the like.

The third block of FIG. 39 shows a rectifier circuit 2404 that mayrectify the AC voltage power from the device resonator into a DCvoltage. In this configuration, the output of the rectifier 2404 may bethe input to a voltage clamp circuit. The voltage clamp circuit (notshown) may limit the maximum voltage at the input to the DC-to-DCconverter 2408D or DC-to-AC converter 2408D. In general, it may bedesirable to use a DC-to-DC/AC converter with a large input voltagedynamic range so that large variations in device position and operationmay be tolerated while adequate power is delivered to the device. Forexample, the voltage level at the output of the rectifier may fluctuateand reach high levels as the power input and load characteristics of thedevice change. As the device performs different tasks it may havevarying power demands. The changing power demands can cause highvoltages at the output of the rectifier as the load characteristicschange. Likewise as the device and the device resonator are broughtcloser and further away from the source, the power delivered to thedevice resonator may vary and cause changes in the voltage levels at theoutput of the rectifier. A voltage clamp circuit may prevent the voltageoutput from the rectifier circuit from exceeding a predetermined valuewhich is within the operating range of the DC-to-DC/AC converter. Thevoltage clamp circuitry may be used to extend the operating modes andranges of a wireless energy transfer system.

The next block of the power and control circuitry of the device is theDC-to-DC converter 2408D that may produce a stable DC output voltage.The DC-to-DC converter may be a boost converter, buck converter,boost-buck converter, single ended primary inductance converter (SEPIC),or any other DC-DC topology that fits the requirements of the particularapplication. If the device requires AC power, a DC-to-AC converter maybe substituted for the DC-to-DC converter, or the DC-to-DC converter maybe followed by a DC-to-AC converter. If the device contains arechargeable battery, the final block of the device power and controlcircuitry may be a battery charge control unit which may manage thecharging and maintenance of the battery in battery powered devices.

The device power and control circuitry 2304 may contain a processor2410D, such as a microcontroller, a digital signal processor, a fieldprogrammable gate array processor, a microprocessor, or any other typeof processor. The processor may be used to read or detect the state orthe operating point of the power and control circuitry and the deviceresonator. The processor may implement algorithms to interpret andadjust the operating point of the circuits, elements, components,subsystems and resonator. The processor may be used to adjust theimpedance matching, the resonator, the DC to DC converters, the DC to ACconverters, the battery charging unit, the rectifier, and the like ofthe wirelessly powered device.

The processor may have wireless or wired data communication links toother devices or sources and may transmit or receive data that can beused to adjust the operating point of the system. Any combination ofpower, voltage, and current signals at a single, or over a range offrequencies, may be monitored at any point in the device circuitry.These signals may be monitored using analog or digital or combinedanalog and digital techniques. These monitored signals may be used infeedback loops or may be reported to the user in a variety of known waysor they may be stored and retrieved at later times. These signals may beused to alert a user of system failures, to indicate performance, or toprovide audio, visual, vibrational, and the like, feedback to a user ofthe system.

FIG. 40 shows components of source power and control circuitry 2302 ofan exemplary wireless power transfer system configured to supply powerto a single or multiple devices. The source power and control circuitry2302 of the exemplary system may be powered from an AC voltage source2502 such as a home electrical outlet, a DC voltage source such as abattery, a USB port of a computer, a solar cell, another wireless powersource, and the like. The source power and control circuitry 2302 maydrive the source resonator 102S with alternating current, such as with afrequency greater than 10 kHz and less than 100 MHz. The source powerand control circuitry 2302 may drive the source resonator 102S withalternating current of frequency less than less than 10 GHz. The sourcepower and control circuitry 2302 may include a DC-to-DC converter 2408S,an AC-to-DC converter 2408S, or both an AC-to-DC converter 2408S and aDC-to-DC 2408S converter, an oscillator 2508, a power amplifier 2504, animpedance matching network 2402S, and the like.

The source power and control circuitry 2302 may be powered from multipleAC-or-DC voltage sources 2502 and may contain AC-to-DC and DC-to-DCconverters 2408S to provide necessary voltage levels for the circuitcomponents as well as DC voltages for the power amplifiers that may beused to drive the source resonator. The DC voltages may be adjustableand may be used to control the output power level of the poweramplifier. The source may contain power factor correction circuitry.

The oscillator 2508 output may be used as the input to a power amplifier2504 that drives the source resonator 102S. The oscillator frequency maybe tunable and the amplitude of the oscillator signal may be varied asone means to control the output power level from the power amplifier.The frequency, amplitude, phase, waveform, and duty cycle of theoscillator signal may be controlled by analog circuitry, by digitalcircuitry or by a combination of analog and digital circuitry. Thecontrol circuitry may include a processor 2410S, such as amicroprocessor, a digital signal processor, a field programmable gatearray processor, and the like.

The impedance matching blocks 2402 of the source and device resonatorsmay be used to tune the power and control circuits and the source anddevice resonators. For example, tuning of these circuits may adjust forperturbation of the quality factor Q of the source or device resonatorsdue to extraneous objects or changes in distance between the source anddevice in a system. Tuning of these circuits may also be used to sensethe operating environment, control power flow to one or more devices, tocontrol power to a wireless power network, to reduce power when unsafeor failure mode conditions are detected, and the like.

Any combination of power, voltage, and current signals may be monitoredat any point in the source circuitry. These signals may be monitoredusing analog or digital or combined analog and digital techniques. Thesemonitored signals may be used in feedback circuits or may be reported tothe user in a variety of known ways or they may be stored and retrievedat later times. These signals may be used to alert a user to systemfailures, to alert a user to exceeded safety thresholds, to indicateperformance, or to provide audio, visual, vibrational, and the like,feedback to a user of the system.

The source power and control circuitry may contain a processor. Theprocessor may be used to read the state or the operating point of thepower and control circuitry and the source resonator. The processor mayimplement algorithms to interpret and adjust the operating point of thecircuits, elements, components, subsystems and resonator. The processormay be used to adjust the impedance matching, the resonator, theDC-to-DC converters, the AC-to-DC converters, the oscillator, the poweramplifier of the source, and the like. The processor and adjustablecomponents of the system may be used to implement frequency and/or timepower delivery multiplexing schemes. The processor may have wireless orwired data communication links to devices and other sources and maytransmit or receive data that can be used to adjust the operating pointof the system.

Although detailed and specific designs are shown in these blockdiagrams, it should be clear to those skilled in the art that manydifferent modifications and rearrangements of the components andbuilding blocks are possible within the spirit of the exemplary system.The division of the circuitry was outlined for illustrative purposes andit should be clear to those skilled in the art that the components ofeach block may be further divided into smaller blocks or merged orshared. In equivalent examples the power and control circuitry may becomposed of individual discrete components or larger integratedcircuits. For example, the rectifier circuitry may be composed ofdiscrete diodes, or use diodes integrated on a single chip. A multitudeof other circuits and integrated devices can be substituted in thedesign depending on design criteria such as power or size or cost orapplication. The whole of the power and control circuitry or any portionof the source or device circuitry may be integrated into one chip.

The impedance matching network of the device and or source may include acapacitor or networks of capacitors, an inductor or networks ofinductors, or any combination of capacitors, inductors, diodes,switches, resistors, and the like. The components of the impedancematching network may be adjustable and variable and may be controlled toaffect the efficiency and operating point of the system. The impedancematching may be performed by controlling the connection point of theresonator, adjusting the permeability of a magnetic material,controlling a bias field, adjusting the frequency of excitation, and thelike. The impedance matching may use or include any number orcombination of varactors, varactor arrays, switched elements, capacitorbanks, switched and tunable elements, reverse bias diodes, air gapcapacitors, compression capacitors, BZT electrically tuned capacitors,MEMS-tunable capacitors, voltage variable dielectrics, transformercoupled tuning circuits, and the like. The variable components may bemechanically tuned, thermally tuned, electrically tuned,piezo-electrically tuned, and the like. Elements of the impedancematching may be silicon devices, gallium nitride devices, siliconcarbide devices and the like. The elements may be chosen to withstandhigh currents, high voltages, high powers, or any combination ofcurrent, voltage and power. The elements may be chosen to be high-Qelements.

The matching and tuning calculations of the source may be performed onan external device through a USB port that powers the device. The devicemay be a computer a PDA or other computational platform.

A demonstration system used a source resonator, coupled to a deviceresonator, to wirelessly power/recharge multiple electronic consumerdevices including, but not limited to, a laptop, a DVD player, aprojector, a cell-phone, a display, a television, a projector, a digitalpicture frame, a light, a TV/DVD player, a portable music player, acircuit breaker, a hand-held tool, a personal digital assistant, anexternal battery charger, a mouse, a keyboard, a camera, an active load,and the like. A variety of devices may be powered simultaneously from asingle device resonator. Device resonators may be operatedsimultaneously as source resonators. The power supplied to a deviceresonator may pass through additional resonators before being deliveredto its intended device resonator.

Monitoring, Feedback and Control

So-called port parameter measurement circuitry may measure or monitorcertain power, voltage, and current, signals in the system andprocessors or control circuits may adjust certain settings or operatingparameters based on those measurements. In addition to these portparameter measurements, the magnitude and phase of voltage and currentsignals, and the magnitude of the power signals, throughout the systemmay be accessed to measure or monitor the system performance. Themeasured signals referred to throughout this disclosure may be anycombination of the port parameter signals, as well as voltage signals,current signals, power signals, and the like. These parameters may bemeasured using analog or digital signals, they may be sampled andprocessed, and they may be digitized or converted using a number ofknown analog and digital processing techniques. Measured or monitoredsignals may be used in feedback circuits or systems to control theoperation of the resonators and/or the system. In general, we refer tothese monitored or measured signals as reference signals, or portparameter measurements or signals, although they are sometimes alsoreferred to as error signals, monitor signals, feedback signals, and thelike. We will refer to the signals that are used to control circuitelements such as the voltages used to drive voltage controlledcapacitors as the control signals.

In some cases the circuit elements may be adjusted to achieve aspecified or predetermined impedance value for the source and deviceresonators. In other cases the impedance may be adjusted to achieve adesired impedance value for the source and device resonators when thedevice resonator is connected to a power consumer or consumers. In othercases the impedance may be adjusted to mitigate changes in the resonantfrequency, or impedance or power level changes owing to movement of thesource and/or device resonators, or changes in the environment (such asthe movement of interacting materials or objects) in the vicinity of theresonators. In other cases the impedance of the source and deviceresonators may be adjusted to different impedance values.

The coupled resonators may be made of different materials and mayinclude different circuits, components and structural designs or theymay be the same. The coupled resonators may include performancemonitoring and measurement circuitry, signal processing and controlcircuitry or a combination of measurement and control circuitry. Some orall of the high-Q magnetic resonators may include tunable impedancecircuits. Some or all of the high-Q magnetic resonators may includeautomatically controlled tunable impedance circuits.

FIG. 41 shows a magnetic resonator with port parameter measurementcircuitry 3802 configured to measure certain parameters of theresonator. The port parameter measurement circuitry may measure theinput impedance of the structure, or the reflected power. Port parametermeasurement circuits may be included in the source and/or deviceresonator designs and may be used to measure two port circuit parameterssuch as S-parameters (scattering parameters), Z-parameters (impedanceparameters), Y-parameters (admittance parameters), T-parameters(transmission parameters), H-parameters (hybrid parameters),ABCD-parameters (chain, cascade or transmission parameters), and thelike. These parameters may be used to describe the electrical behaviorof linear electrical networks when various types of signals are applied.

Different parameters may be used to characterize the electrical networkunder different operating or coupling scenarios. For example,S-parameters may be used to measure matched and unmatched loads. Inaddition, the magnitude and phase of voltage and current signals withinthe magnetic resonators and/or within the sources and devices themselvesmay be monitored at a variety of points to yield system performanceinformation. This information may be presented to users of the systemvia a user interface such as a light, a read-out, a beep, a noise, avibration or the like, or it may be presented as a digital signal or itmay be provided to a processor in the system and used in the automaticcontrol of the system. This information may be logged, stored, or may beused by higher level monitoring and control systems.

FIG. 42 shows a circuit diagram of a magnetic resonator where thetunable impedance network may be realized with voltage controlledcapacitors 3902 or capacitor networks. Such an implementation may beadjusted, tuned or controlled by electrical circuits and/or computerprocessors, such as a programmable voltage source 3908, and the like.For example, the voltage controlled capacitors may be adjusted inresponse to data acquired by the port parameter measurement circuitry3802 and processed by a measurement analysis and control algorithmsubsystem 3904. Reference signals may be derived from the port parametermeasurement circuitry or other monitoring circuitry designed to measurethe degree of deviation from a desired system operating point. Themeasured reference signals may include voltage, current,complex-impedance, reflection coefficient, power levels and the like, atone or several points in the system and at a single frequency or atmultiple frequencies.

The reference signals may be fed to measurement analysis and controlalgorithm subsystem modules that may generate control signals to changethe values of various components in a tunable impedance matchingnetwork. The control signals may vary the resonant frequency and/or theinput impedance of the magnetic resonator, or the power level suppliedby the source, or the power level drawn by the device, to achieve thedesired power exchange between power supplies/generators and powerdrains/loads.

Adjustment algorithms may be used to adjust the frequency and/orimpedance of the magnetic resonators. The algorithms may take inreference signals related to the degree of deviation from a desiredoperating point for the system and output correction or control signalsrelated to that deviation that control variable or tunable elements ofthe system to bring the system back towards the desired operating pointor points. The reference signals for the magnetic resonators may beacquired while the resonators are exchanging power in a wireless powertransmission system, or they may be switched out of the circuit duringsystem operation. Corrections to the system may be applied or performedcontinuously, periodically, upon a threshold crossing, digitally, usinganalog methods, and the like.

FIG. 43 shows an end-to-end wireless power transmission system. Both thesource and the device may include port measurement circuitry 3802 and aprocessor 2410. The box labeled “coupler/switch” 4002 indicates that theport measurement circuitry 3802 may be connected to the resonator 102 bya directional coupler or a switch, enabling the measurement, adjustmentand control of the source and device resonators to take place inconjunction with, or separate from, the power transfer functionality.

The port parameter measurement and/or processing circuitry may residewith some, any, or all resonators in a system. The port parametermeasurement circuitry may utilize portions of the power transmissionsignal or may utilize excitation signals over a range of frequencies tomeasure the source/device resonator response (i.e. transmission andreflection between any two ports in the system), and may containamplitude and/or phase information. Such measurements may be achievedwith a swept single frequency signal or a multi-frequency signal. Thesignals used to measure and monitor the resonators and the wirelesspower transmission system may be generated by a processor or processorsand standard input/output (I/O) circuitry including digital to analogconverters (DACs), analog to digital converters (ADCs), amplifiers,signal generation chips, passive components and the like. Measurementsmay be achieved using test equipment such as a network analyzer or usingcustomized circuitry. The measured reference signals may be digitized byADCs and processed using customized algorithms running on a computer, amicroprocessor, a DSP chip, an ASIC, and the like. The measuredreference signals may be processed in an analog control loop.

The measurement circuitry may measure any set of two port parameterssuch as S-parameters, Y-parameters, Z-parameters, H-parameters,G-parameters, T-parameters, ABCD-parameters, and the like. Measurementcircuitry may be used to characterize current and voltage signals atvarious points in the drive and resonator circuitry, the impedanceand/or admittance of the source and device resonators at opposite endsof the system, i.e. looking into the source resonator matching network(“port 1” in FIG. 43) towards the device and vice versa.

The device may measure relevant signals and/or port parameters,interpret the measurement data, and adjust its matching network tooptimize the impedance looking into the coupled system independently ofthe actions of the source. The source may measure relevant portparameters, interpret the measurement data, and adjust its matchingnetwork to optimize the impedance looking into the coupled systemindependently of the actions of the device.

FIG. 43 shows a block diagram of a source and device in a wireless powertransmission system. The system may be configured to execute a controlalgorithm that actively adjusts the tuning/matching networks in eitherof or both the source and device resonators to optimize performance inthe coupled system. Port measurement circuitry 3802S may measure signalsin the source and communicate those signals to a processor 2410. Aprocessor 2410 may use the measured signals in a performanceoptimization or stabilization algorithm and generate control signalsbased on the outputs of those algorithms. Control signals may be appliedto variable circuit elements in the tuning/impedance matching circuits2402S to adjust the source's operating characteristics, such as power inthe resonator and coupling to devices. Control signals may be applied tothe power supply or generator to turn the supply on or off, to increaseor decrease the power level, to modulate the supply signal and the like.

The power exchanged between sources and devices may depend on a varietyof factors. These factors may include the effective impedance of thesources and devices, the Q's of the sources and devices, the resonantfrequencies of the sources and devices, the distances between sourcesand devices, the interaction of materials and objects in the vicinity ofsources and devices and the like. The port measurement circuitry andprocessing algorithms may work in concert to adjust the resonatorparameters to maximize power transfer, to hold the power transferconstant, to controllably adjust the power transfer, and the like, underboth dynamic and steady state operating conditions.

Some, all or none of the sources and devices in a system implementationmay include port measurement circuitry 3802S and processing 2410capabilities. FIG. 44 shows an end-to-end wireless power transmissionsystem in which only the source 102S contains port measurement circuitry3802 and a processor 2410S. In this case, the device resonator 102Doperating characteristics may be fixed or may be adjusted by analogcontrol circuitry and without the need for control signals generated bya processor.

FIG. 45 shows an end-to-end wireless power transmission system. Both thesource and the device may include port measurement circuitry 3802 but inthe system of FIG. 45, only the source contains a processor 2410S. Thesource and device may be in communication with each other and theadjustment of certain system parameters may be in response to controlsignals that have been wirelessly communicated, such as though wirelesscommunications circuitry 4202, between the source and the device. Thewireless communication channel 4204 may be separate from the wirelesspower transfer channel 4208, or it may be the same. That is, theresonators 102 used for power exchange may also be used to exchangeinformation. In some cases, information may be exchanged by modulating acomponent a source or device circuit and sensing that change with portparameter or other monitoring equipment.

Implementations where only the source contains a processor 2410 may bebeneficial for multi-device systems where the source can handle all ofthe tuning and adjustment “decisions” and simply communicate the controlsignals back to the device(s). This implementation may make the devicesmaller and cheaper because it may eliminate the need for, or reduce therequired functionality of, a processor in the device. A portion of or anentire data set from each port measurement at each device may be sentback to the source microprocessor for analysis, and the controlinstructions may be sent back to the devices. These communications maybe wireless communications.

FIG. 46 shows an end-to-end wireless power transmission system. In thisexample, only the source contains port measurement circuitry 3802 and aprocessor 2410S. The source and device may be in communication, such asvia wireless communication circuitry 4202, with each other and theadjustment of certain system parameters may be in response to controlsignals that have been wirelessly communicated between the source andthe device.

FIG. 47 shows coupled electromagnetic resonators 102 whose frequency andimpedance may be automatically adjusted using a processor or a computer.Resonant frequency tuning and continuous impedance adjustment of thesource and device resonators may be implemented with reverse biaseddiodes, Schottky diodes and/or varactor elements contained within thecapacitor networks shown as C1, C2, and C3 in FIG. 47. The circuittopology that was built and demonstrated and is described here isexemplary and is not meant to limit the discussion of automatic systemtuning and control in any way. Other circuit topologies could beutilized with the measurement and control architectures discussed inthis disclosure.

Device and source resonator impedances and resonant frequencies may bemeasured with a network analyzer 4402A-B, or by other means describedabove, and implemented with a controller, such as with Lab View 4404.The measurement circuitry or equipment may output data to a computer ora processor that implements feedback algorithms and dynamically adjuststhe frequencies and impedances via a programmable DC voltage source.

In one arrangement, the reverse biased diodes (Schottky, semiconductorjunction, and the like) used to realize the tunable capacitance drewvery little DC current and could be reverse biased by amplifiers havinglarge series output resistances. This implementation may enable DCcontrol signals to be applied directly to the controllable circuitelements in the resonator circuit while maintaining a very high-Q in themagnetic resonator.

C2 biasing signals may be isolated from C1 and/or C3 biasing signalswith a DC blocking capacitor as shown in FIG. 47, if the required DCbiasing voltages are different. The output of the biasing amplifiers maybe bypassed to circuit ground to isolate RF voltages from the biasingamplifiers, and to keep non-fundamental RF voltages from being injectedinto the resonator. The reverse bias voltages for some of the capacitorsmay instead be applied through the inductive element in the resonatoritself, because the inductive element acts as a short circuit at DC.

The port parameter measurement circuitry may exchange signals with aprocessor (including any required ADCs and DACs) as part of a feedbackor control system that is used to automatically adjust the resonantfrequency, input impedance, energy stored or captured by the resonatoror power delivered by a source or to a device load. The processor mayalso send control signals to tuning or adjustment circuitry in orattached to the magnetic resonator.

When utilizing varactors or diodes as tunable capacitors, it may bebeneficial to place fixed capacitors in parallel and in series with thetunable capacitors operating at high reverse bias voltages in thetuning/matching circuits. This arrangement may yield improvements incircuit and system stability and in power handling capability byoptimizing the operating voltages on the tunable capacitors.

Varactors or other reverse biased diodes may be used as a voltagecontrolled capacitor. Arrays of varactors may be used when highervoltage compliance or different capacitance is required than that of asingle varactor component. Varactors may be arranged in an N by M arrayconnected serially and in parallel and treated as a single two terminalcomponent with different characteristics than the individual varactorsin the array. For example, an N by N array of equal varactors wherecomponents in each row are connected in parallel and components in eachcolumn are connected in series may be used as a two terminal device withthe same capacitance as any single varactor in the array but with avoltage compliance that is N times that of a single varactor in thearray. Depending on the variability and differences of parameters of theindividual varactors in the array additional biasing circuits composedof resistors, inductors, and the like may be needed. A schematic of afour by four array of unbiased varactors 4502 that may be suitable formagnetic resonator applications is shown in FIG. 48.

Further improvements in system performance may be realized by carefulselection of the fixed value capacitor(s) that are placed in paralleland/or in series with the tunable (varactor/diode/capacitor) elements.Multiple fixed capacitors that are switched in or out of the circuit maybe able to compensate for changes in resonator Q's, impedances, resonantfrequencies, power levels, coupling strengths, and the like, that mightbe encountered in test, development and operational wireless powertransfer systems. Switched capacitor banks and other switched elementbanks may be used to assure the convergence to the operating frequenciesand impedance values required by the system design.

An exemplary control algorithm for isolated and coupled magneticresonators may be described for the circuit and system elements shown inFIG. 47. One control algorithm first adjusts each of the source anddevice resonator loops “in isolation”, that is, with the otherresonators in the system “shorted out” or “removed” from the system. Forpractical purposes, a resonator can be “shorted out” by making itresonant at a much lower frequency such as by maximizing the value of C1and/or C3. This step effectively reduces the coupling between theresonators, thereby effectively reducing the system to a singleresonator at a particular frequency and impedance.

Tuning a magnetic resonator in isolation includes varying the tunableelements in the tuning and matching circuits until the values measuredby the port parameter measurement circuitry are at their predetermined,calculated or measured relative values. The desired values for thequantities measured by the port parameter measurement circuitry may bechosen based on the desired matching impedance, frequency, strongcoupling parameter, and the like. For the exemplary algorithms disclosedbelow, the port parameter measurement circuitry measures S-parametersover a range of frequencies. The range of frequencies used tocharacterize the resonators may be a compromise between the systemperformance information obtained and computation/measurement speed. Forthe algorithms described below the frequency range may be approximately+/−20% of the operating resonant frequency.

Each isolated resonator may be tuned as follows. First, short out theresonator not being adjusted. Next minimize C1, C2, and C3, in theresonator that is being characterized and adjusted. In most cases therewill be fixed circuit elements in parallel with C1, C2, and C3, so thisstep does not reduce the capacitance values to zero. Next, startincreasing C2 until the resonator impedance is matched to the “target”real impedance at any frequency in the range of measurement frequenciesdescribed above. The initial “target” impedance may be less than theexpected operating impedance for the coupled system.

C2 may be adjusted until the initial “target” impedance is realized fora frequency in the measurement range. Then C1 and/or C3 may be adjusteduntil the loop is resonant at the desired operating frequency.

Each resonator may be adjusted according to the above algorithm. Aftertuning each resonator in isolation, a second feedback algorithm may beapplied to optimize the resonant frequencies and/or input impedances forwirelessly transferring power in the coupled system.

The required adjustments to C1 and/or C2 and/or C3 in each resonator inthe coupled system may be determined by measuring and processing thevalues of the real and imaginary parts of the input impedance fromeither and/or both “port(s)” shown in FIG. 43. For coupled resonators,changing the input impedance of one resonator may change the inputimpedance of the other resonator. Control and tracking algorithms mayadjust one port to a desired operating point based on measurements atthat port, and then adjust the other port based on measurements at thatother port. These steps may be repeated until both sides converge to thedesired operating point.

S-parameters may be measured at both the source and device ports and thefollowing series of measurements and adjustments may be made. In thedescription that follows, Z₀ is an input impedance and may be the targetimpedance. In some cases Z₀ is 50 ohms or is near 50 ohms. Z₁ and Z₂ areintermediate impedance values that may be the same value as Z₀ or may bedifferent than Z₀. Re{value} means the real part of a value andIm{value} means the imaginary part of a value.

An algorithm that may be used to adjust the input impedance and resonantfrequency of two coupled resonators is set forth below:

1) Adjust each resonator “in isolation” as described above. 2) Adjustsource C1/C3 until, at ω_(o) , Re{S11} = (Z₁ +/− ε_(Re)) as follows: -If Re{S11 @ω_(o) } > (Z₁ + ε_(Re)), decrease C1/C3. If Re{S11 @ω_(o) } <(Zo − ε_(Re)), increase C1/C3. 3) Adjust source C2 until, at ω_(o) ,Im{S11} = (+/− ε_(Im)) as follows: - If Im{S11 @ ω_(o) } > ε_(Im),decrease C2. If Im{S11 @ ω_(o) } < − ε_(Im) , increase C2. 4) Adjustdevice C1/C3 until, at ω₀, Re{S22} = (Z₂ +/− ε_(Re)) as follows: - IfRe{S22 @ ω_(o) } > (Z₂ + ε_(Re)), decrease C1/C3. If Re{S22 @ ω_(o) } <(Zo − ε_(Re)), increase C1/C3. 5) Adjust device C2 until, at ω_(o) ,Im{S22} = 0 as follows: - If Im{S22 @ ω_(o) } > ε_(Im), decrease C2. IfIm{S22 @ ω_(o) } < −ε_(Im) , increase C2.

We have achieved a working system by repeating steps 1-4 until both(Re{S11}, Im{S11}) and (Re{S22}, Im{S22}) converge to ((Z₀+/−∈_(Re)),(+/−∈_(Im))) at ω_(o), where Z₀ is the desired matching impedance andω_(o) is the desired operating frequency. Here, ∈_(Im) represents themaximum deviation of the imaginary part, at ω_(o), from the desiredvalue of 0, and ∈_(Re) represents the maximum deviation of the real partfrom the desired value of Z₀. It is understood that ∈_(Im) and ∈_(Re)can be adjusted to increase or decrease the number of steps toconvergence at the potential cost of system performance (efficiency). Itis also understood that steps 1-4 can be performed in a variety ofsequences and a variety of ways other than that outlined above (i.e.first adjust the source imaginary part, then the source real part; orfirst adjust the device real part, then the device imaginary part, etc.)The intermediate impedances Z₁ and Z₂ may be adjusted during steps 1-4to reduce the number of steps required for convergence. The desire ortarget impedance value may be complex, and may vary in time or underdifferent operating scenarios.

Steps 1-4 may be performed in any order, in any combination and anynumber of times. Having described the above algorithm, variations to thesteps or the described implementation may be apparent to one of ordinaryskill in the art. The algorithm outlined above may be implemented withany equivalent linear network port parameter measurements (i.e.,Z-parameters, Y-parameters, T-parameters, H-parameters, ABCD-parameters,etc.) or other monitor signals described above, in the same way thatimpedance or admittance can be alternatively used to analyze a linearcircuit to derive the same result.

The resonators may need to be retuned owing to changes in the “loaded”resistances, Rs and Rd, caused by changes in the mutual inductance M(coupling) between the source and device resonators. Changes in theinductances, Ls and Ld, of the inductive elements themselves may becaused by the influence of external objects, as discussed earlier, andmay also require compensation. Such variations may be mitigated by theadjustment algorithm described above.

A directional coupler or a switch may be used to connect the portparameter measurement circuitry to the source resonator andtuning/adjustment circuitry. The port parameter measurement circuitrymay measure properties of the magnetic resonator while it is exchangingpower in a wireless power transmission system, or it may be switched outof the circuit during system operation. The port parameter measurementcircuitry may measure the parameters and the processor may controlcertain tunable elements of the magnetic resonator at start-up, or atcertain intervals, or in response to changes in certain system operatingparameters.

A wireless power transmission system may include circuitry to vary ortune the impedance and/or resonant frequency of source and deviceresonators. Note that while tuning circuitry is shown in both the sourceand device resonators, the circuitry may instead be included in only thesource or the device resonators, or the circuitry may be included inonly some of the source and/or device resonators. Note too that while wemay refer to the circuitry as “tuning” the impedance and or resonantfrequency of the resonators, this tuning operation simply means thatvarious electrical parameters such as the inductance or capacitance ofthe structure are being varied. In some cases, these parameters may bevaried to achieve a specific predetermined value, in other cases theymay be varied in response to a control algorithm or to stabilize atarget performance value that is changing. In some cases, the parametersare varied as a function of temperature, of other sources or devices inthe area, of the environment, at the like.

Applications

For each listed application, it will be understood by one of ordinaryskill-in-the-art that there are a variety of ways that the resonatorstructures used to enable wireless power transmission may be connectedor integrated with the objects that are supplying or being powered. Theresonator may be physically separate from the source and device objects.The resonator may supply or remove power from an object usingtraditional inductive techniques or through direct electricalconnection, with a wire or cable for example. The electrical connectionmay be from the resonator output to the AC or DC power input port on theobject. The electrical connection may be from the output power port ofan object to the resonator input.

FIG. 49 shows a source resonator 4904 that is physically separated froma power supply and a device resonator 4902 that is physically separatedfrom the device 4900, in this illustration a laptop computer. Power maybe supplied to the source resonator, and power may be taken from thedevice resonator directly, by an electrical connection. One of ordinaryskill in the art will understand from the materials incorporated byreference that the shape, size, material composition, arrangement,position and orientation of the resonators above are provided by way ofnon-limiting example, and that a wide variation in any and all of theseparameters could be supported by the disclosed technology for a varietyof applications.

Continuing with the example of the laptop, and without limitation, thedevice resonator may be physically connected to the device it ispowering or charging. For example, as shown in FIG. 50 a and FIG. 50 b,the device resonator 5002 may be (a) integrated into the housing of thedevice 5000 or (b) it may be attached by an adapter. The resonator 5002may (FIG. 50 b-d) or may not (FIG. 50 a) be visible on the device. Theresonator may be affixed to the device, integrated into the device,plugged into the device, and the like.

The source resonator may be physically connected to the source supplyingthe power to the system. As described above for the devices and deviceresonators, there are a variety of ways the resonators may be attachedto, connected to or integrated with the power supply. One of ordinaryskill in the art will understand that there are a variety of ways theresonators may be integrated in the wireless power transmission system,and that the sources and devices may utilize similar or differentintegration techniques.

Continuing again with the example of the laptop computer, and withoutlimitation, the laptop computer may be powered, charged or recharged bya wireless power transmission system. A source resonator may be used tosupply wireless power and a device resonator may be used to capture thewireless power. A device resonator 5002 may be integrated into the edgeof the screen (display) as illustrated in FIG. 50 d, and/or into thebase of the laptop as illustrated in FIG. 50 c. The source resonator5002 may be integrated into the base of the laptop and the deviceresonator may be integrated into the edge of the screen. The resonatorsmay also or instead be affixed to the power source and/or the laptop.The source and device resonators may also or instead be physicallyseparated from the power supply and the laptop and may be electricallyconnected by a cable. The source and device resonators may also orinstead be physically separated from the power supply and the laptop andmay be electrically coupled using a traditional inductive technique. Oneof ordinary skill in the art will understand that, while the precedingexamples relate to wireless power transmission to a laptop, that themethods and systems disclosed for this application may be suitablyadapted for use with other electrical or electronic devices. In general,the source resonator may be external to the source and supplying powerto a device resonator that in turn supplies power the device, or thesource resonator may be connected to the source and supplying power to adevice resonator that in turn supplies power to a portion of the device,or the source resonator may internal to the source and supplying powerto a device resonator that in turn supplies power to a portion of thedevice, as well as any combination of these.

A system or method disclosed herein may provide power to an electricalor electronics device, such as, and not limited to, phones, cell phones,cordless phones, smart phones, PDAs, audio devices, music players, MP3players, radios, portable radios and players, wireless headphones,wireless headsets, computers, laptop computers, wireless keyboards,wireless mouse, televisions, displays, flat screen displays, computerdisplays, displays embedded in furniture, digital picture frames,electronic books, (e.g. the Kindle, e-ink books, magazines, and thelike), remote control units (also referred to as controllers, gamecontrollers, commanders, clickers, and the like, and used for the remotecontrol of a plurality of electronics devices, such as televisions,video games, displays, computers, audio visual equipment, lights, andthe like), lighting devices, cooling devices, air circulation devices,purification devices, personal hearing aids, power tools, securitysystems, alarms, bells, flashing lights, sirens, sensors, loudspeakers,electronic locks, electronic keypads, light switches, other electricalswitches, and the like. Here the term electronic lock is used toindicate a door lock which operates electronically (e.g. with electroniccombo-key, magnetic card, RFID card, and the like) which is placed on adoor instead of a mechanical key-lock. Such locks are often batteryoperated, risking the possibility that the lock might stop working whena battery dies, leaving the user locked-out. This may be avoided wherethe battery is either charged or completely replaced by a wireless powertransmission implementation as described herein.

Here, the term light switch (or other electrical switch) is meant toindicate any switch (e.g. on a wall of a room) in one part of the roomthat turns on/off a device (e.g. light fixture at the center of theceiling) in another part of the room. To install such a switch by directconnection, one would have to run a wire all the way from the device tothe switch. Once such a switch is installed at a particular spot, it maybe very difficult to move. Alternately, one can envision a ‘wirelessswitch’, where “wireless” means the switching (on/off) commands arecommunicated wirelessly, but such a switch has traditionally required abattery for operation. In general, having too many battery operatedswitches around a house may be impractical, because those many batterieswill need to be replaced periodically. So, a wirelessly communicatingswitch may be more convenient, provided it is also wirelessly powered.For example, there already exist communications wireless door-bells thatare battery powered, but where one still has to replace the battery inthem periodically. The remote doorbell button may be made to becompletely wireless, where there may be no need to ever replace thebattery again. Note that here, the term ‘cordless’ or ‘wireless’ or‘communications wireless’ is used to indicate that there is a cordlessor wireless communications facility between the device and anotherelectrical component, such as the base station for a cordless phone, thecomputer for a wireless keyboard, and the like. One skilled in the artwill recognize that any electrical or electronics device may include awireless communications facility, and that the systems and methodsdescribed herein may be used to add wireless power transmission to thedevice. As described herein, power to the electrical or electronicsdevice may be delivered from an external or internal source resonator,and to the device or portion of the device. Wireless power transmissionmay significantly reduce the need to charge and/or replace batteries fordevices that enter the near vicinity of the source resonator and therebymay reduce the downtime, cost and disposal issues often associated withbatteries.

The systems and methods described herein may provide power to lightswithout the need for either wired power or batteries. That is, thesystems and methods described herein may provide power to lights withoutwired connection to any power source, and provide the energy to thelight non-radiatively across mid-range distances, such as across adistance of a quarter of a meter, one meter, three meters, and the like.A ‘light’ as used herein may refer to the light source itself, such asan incandescent light bulb, florescent light bulb lamps, Halogen lamps,gas discharge lamps, fluorescent lamps, neon lamps, high-intensitydischarge lamps, sodium vapor lamps, Mercury-vapor lamps,electroluminescent lamps, light emitting diodes (LED) lamps, and thelike; the light as part of a light fixture, such as a table lamp, afloor lamp, a ceiling lamp, track lighting, recessed light fixtures, andthe like; light fixtures integrated with other functions, such as alight/ceiling fan fixture, and illuminated picture frame, and the like.As such, the systems and methods described herein may reduce thecomplexity for installing a light, such as by minimizing theinstallation of electrical wiring, and allowing the user to place ormount the light with minimal regard to sources of wired power. Forinstance, a light may be placed anywhere in the vicinity of a sourceresonator, where the source resonator may be mounted in a plurality ofdifferent places with respect to the location of the light, such as onthe floor of the room above, (e.g. as in the case of a ceiling light andespecially when the room above is the attic); on the wall of the nextroom, on the ceiling of the room below, (e.g. as in the case of a floorlamp); in a component within the room or in the infrastructure of theroom as described herein; and the like. For example, a light/ceiling fancombination is often installed in a master bedroom, and the masterbedroom often has the attic above it. In this instance a user may moreeasily install the light/ceiling fan combination in the master bedroom,such as by simply mounting the light/ceiling fan combination to theceiling, and placing a source coil (plugged into the house wired ACpower) in the attic above the mounted fixture. In another example, thelight may be an external light, such as a flood light or security light,and the source resonator mounted inside the structure. This way ofinstalling lighting may be particularly beneficial to users who renttheir homes, because now they may be able to mount lights and such otherelectrical components without the need to install new electrical wiring.The control for the light may also be communicated by near-fieldcommunications as described herein, or by traditional wirelesscommunications methods.

The systems and methods described herein may provide power from a sourceresonator to a device resonator that is either embedded into the devicecomponent, or outside the device component, such that the devicecomponent may be a traditional electrical component or fixture. Forinstance, a ceiling lamp may be designed or retrofitted with a deviceresonator integrated into the fixture, or the ceiling lamp may be atraditional wired fixture, and plugged into a separate electricalfacility equipped with the device resonator. In an example, theelectrical facility may be a wireless junction box designed to have adevice resonator for receiving wireless power, say from a sourceresonator placed on the floor of the room above (e.g. the attic), andwhich contains a number of traditional outlets that are powered from thedevice resonator. The wireless junction box, mounted on the ceiling, maynow provide power to traditional wired electrical components on theceiling (e.g. a ceiling light, track lighting, a ceiling fan). Thus, theceiling lamp may now be mounted to the ceiling without the need to runwires through the infrastructure of the building. This type of deviceresonator to traditional outlet junction box may be used in a pluralityof applications, including being designed for the interior or exteriorof a building, to be made portable, made for a vehicle, and the like.Wireless power may be transferred through common building materials,such as wood, wall board, insulation, glass. brick, stone, concrete, andthe like. The benefits of reduced installation cost, re-configurability,and increased application flexibility may provide the user significantbenefits over traditional wired installations. The device resonator fora traditional outlet junction box may include a plurality of electricalcomponents for facilitating the transfer of power from the deviceresonator to the traditional outlets, such as power source electronicswhich convert the specific frequencies needed to implement efficientpower transfer to line voltage, power capture electronics which mayconvert high frequency AC to usable voltage and frequencies (AC and/orDC), controls which synchronize the capture device and the power outputand which ensure consistent, safe, and maximally efficient powertransfer, and the like.

The systems and methods described herein may provide advantages tolights or electrical components that operate in environments that arewet, harsh, controlled, and the like, such has outside and exposed tothe rain, in a pool/sauna/shower, in a maritime application, inhermetically sealed components, in an explosive-proof room, on outsidesignage, a harsh industrial environment in a volatile environment (e.g.from volatile vapors or airborne organics, such as in a grain silo orbakery), and the like. For example, a light mounted under the waterlevel of a pool is normally difficult to wire up, and is required to bewater-sealed despite the need for external wires. But a pool light usingthe principles disclosed herein may more easily be made water sealed, asthere may be no external wires needed. In another example, an explosionproof room, such as containing volatile vapors, may not only need to behermetically sealed, but may need to have all electrical contacts (thatcould create a spark) sealed. Again, the principles disclosed herein mayprovide a convenient way to supply sealed electrical components for suchapplications.

The systems and methods disclosed herein may provide power to gamecontroller applications, such as to a remote handheld game controller.These game controllers may have been traditionally powered solely bybatteries, where the game controller's use and power profile causedfrequent changing of the battery, battery pack, rechargeable batteries,and the like, that may not have been ideal for the consistent use to thegame controller, such as during extended game play. A device resonatormay be placed into the game controller, and a source resonator,connected to a power source, may be placed in the vicinity. Further, thedevice resonator in the game controller may provide power directly tothe game controller electronics without a battery; provide power to abattery, battery pack, rechargeable battery, and the like, which thenprovides power to the game controller electronics; and the like. Thegame controller may utilize multiple battery packs, where each batterypack is equipped with a device resonator, and thus may be constantlyrecharging while in the vicinity of the source resonator, whetherplugged into the game controller or not. The source resonator may beresident in a main game controller facility for the game, where the maingame controller facility and source resonator are supplied power from AC‘house’ power; resident in an extension facility form AC power, such asin a source resonator integrated into an ‘extension cord’; resident in agame chair, which is at least one of plugged into the wall AC, pluggedinto the main game controller facility, powered by a battery pack in thegame chair; and the like. The source resonator may be placed andimplemented in any of the configurations described herein.

The systems and methods disclosed herein may integrate device resonatorsinto battery packs, such as battery packs that are interchangeable withother battery packs. For instance, some portable devices may use upelectrical energy at a high rate such that a user may need to havemultiple interchangeable battery packs on hand for use, or the user mayoperate the device out of range of a source resonator and needadditional battery packs to continue operation, such as for power tools,portable lights, remote control vehicles, and the like. The use of theprinciples disclosed herein may not only provide a way for deviceresonator enabled battery packs to be recharged while in use and inrange, but also for the recharging of battery packs not currently in useand placed in range of a source resonator. In this way, battery packsmay always be ready to use when a user runs down the charge of a batterypack being used. For example, a user may be working with a wirelesspower tool, where the current requirements may be greater than can berealized through direct powering from a source resonator. In this case,despite the fact that the systems and methods described herein may beproviding charging power to the in-use battery pack while in range, thebattery pack may still run down, as the power usage may have exceededthe recharge rate. Further, the user may simply be moving in and out ofrange, or be completely out of range while using the device. However,the user may have placed additional battery packs in the vicinity of thesource resonator, which have been recharged while not in use, and arenow charged sufficiently for use. In another example, the user may beworking with the power tool away from the vicinity of the sourceresonator, but leave the supplemental battery packs to charge in thevicinity of the source resonator, such as in a room with a portablesource resonator or extension cord source resonator, in the user'svehicle, in user's tool box, and the like. In this way, the user may nothave to worry about taking the time to, and/or remembering to plug intheir battery packs for future use. The user may only have to change outthe used battery pack for the charged battery pack and place the usedone in the vicinity of the source resonator for recharging. Deviceresonators may be built into enclosures with known battery form factorsand footprints and may replace traditional chemical batteries in knowndevices and applications. For example, device resonators may be builtinto enclosures with mechanical dimensions equivalent to AA batteries,AAA batteries, D batteries, 9V batteries, laptop batteries, cell phonebatteries, and the like. The enclosures may include a smaller “buttonbattery” in addition to the device resonator to store charge and provideextended operation, either in terms of time or distance. Other energystorage devices in addition to or instead of button batteries may beintegrated with the device resonators and any associated powerconversion circuitry. These new energy packs may provide similar voltageand current levels as provided by traditional batteries, but may becomposed of device resonators, power conversion electronics, a smallbattery, and the like. These new energy packs may last longer thantraditional batteries because they may be more easily recharged and maybe recharging constantly when they are located in a wireless power zone.In addition, such energy packs may be lighter than traditionalbatteries, may be safer to use and store, may operate over widertemperature and humidity ranges, may be less harmful to the environmentwhen thrown away, and the like. As described herein, these energy packsmay last beyond the life of the product when used in wireless powerzones as described herein.

The systems and methods described herein may be used to power visualdisplays, such as in the case of the laptop screen, but more generallyto include the great variety and diversity of displays utilized intoday's electrical and electronics components, such as in televisions,computer monitors, desktop monitors, laptop displays, digital photoframes, electronic books, mobile device displays (e.g. on phones, PDAs,games, navigation devices, DVD players), and the like. Displays that maybe powered through one or more of the wireless power transmissionsystems described herein may also include embedded displays, such asembedded in electronic components (e.g. audio equipment, homeappliances, automotive displays, entertainment devices, cash registers,remote controls), in furniture, in building infrastructure, in avehicle, on the surface of an object (e.g. on the surface of a vehicle,building, clothing, signs, transportation), and the like. Displays maybe very small with tiny resonant devices, such as in a smart card asdescribed herein, or very large, such as in an advertisement sign.Displays powered using the principles disclosed herein may also be anyone of a plurality of imaging technologies, such as liquid crystaldisplay (LCD), thin film transistor LCD, passive LCD, cathode ray tube(CRT), plasma display, projector display (e.g. LCD, DLP, LCOS),surface-conduction electron-emitter display (SED), organiclight-emitting diode (OLED), and the like. Source coil configurationsmay include attaching to a primary power source, such as building power,vehicle power, from a wireless extension cord as described herein, andthe like; attached to component power, such as the base of an electricalcomponent (e.g. the base of a computer, a cable box for a TV); anintermediate relay source coil; and the like. For example, hanging adigital display on the wall may be very appealing, such as in the caseof a digital photo frame that receives its information signalswirelessly or through a portable memory device, but the need for anunsightly power cord may make it aesthetically unpleasant. However, witha device coil embedded in the digital photo frame, such as wrappedwithin the frame portion, may allow the digital photo frame to be hungwith no wires at all. The source resonator may then be placed in thevicinity of the digital photo frame, such as in the next room on theother side of the wall, plugged directly into a traditional poweroutlet, from a wireless extension cord as described herein, from acentral source resonator for the room, and the like.

The systems and methods described herein may provide wireless powertransmission between different portions of an electronics facility.Continuing with the example of the laptop computer, and withoutlimitation, the screen of the laptop computer may require power from thebase of the laptop. In this instance, the electrical power has beentraditionally routed via direct electrical connection from the base ofthe laptop to the screen over a hinged portion of the laptop between thescreen and the base. When a wired connection is utilized, the wiredconnection may tend to wear out and break, the design functionality ofthe laptop computer may be limited by the required direct electricalconnection, the design aesthetics of the laptop computer may be limitedby the required direct electrical connection, and the like. However, awireless connection may be made between the base and the screen. In thisinstance, the device resonator may be placed in the screen portion topower the display, and the base may be either powered by a second deviceresonator, by traditional wired connections, by a hybrid ofresonator-battery-direct electrical connection, and the like. This maynot only improve the reliability of the power connection due to theremoval of the physical wired connection, but may also allow designersto improve the functional and/or aesthetic design of the hinge portionof the laptop in light of the absence of physical wires associated withthe hinge. Again, the laptop computer has been used here to illustratehow the principles disclosed herein may improve the design of anelectric or electronic device, and should not be taken as limiting inany way. For instance, many other electrical devices with separatedphysical portions could benefit from the systems and methods describedherein, such as a refrigerator with electrical functions on the door,including an ice maker, a sensor system, a light, and the like; a robotwith movable portions, separated by joints; a car's power system and acomponent in the car's door; and the like. The ability to provide powerto a device via a device resonator from an external source resonator, orto a portion of the device via a device resonator from either externalor internal source resonators, will be recognized by someone skilled inthe art to be widely applicable across the range of electric andelectronic devices.

The systems and methods disclosed herein may provide for a sharing ofelectrical power between devices, such as between charged devices anduncharged devices. For instance a charged up device or appliance may actlike a source and send a predetermined amount of energy, dialed inamount of energy, requested and approved amount of energy, and the like,to a nearby device or appliance. For example, a user may have a cellphone and a digital camera that are both capable of transmitting andreceiving power through embedded source and device resonators, and oneof the devices, say the cell phone, is found to be low on charge. Theuser may then transfer charge from the digital camera to the cell phone.The source and device resonators in these devices may utilize the samephysical resonator for both transmission and reception, utilize separatesource and device resonators, one device may be designed to receive andtransmit while the other is designed to receive only, one device may bedesigned to transmit only and the other to receive only, and the like.

To prevent complete draining the battery of a device it may have asetting allowing a user to specify how much of the power resource thereceiving device is entitled to. It may be useful, for example, to put alimit on the amount of power available to external devices and to havethe ability to shut down power transmission when battery power fallsbelow a threshold.

The systems and methods described herein may provide wireless powertransfer to a nearby electrical or electronics component in associationwith an electrical facility, where the source resonator is in theelectrical facility and the device resonator is in the electronicscomponent. The source resonator may also be connected to, plugged into,attached to the electrical facility, such as through a universalinterface (e.g. a USB interface, PC card interface), supplementalelectrical outlet, universal attachment point, and the like, of theelectrical facility. For example, the source resonator may be inside thestructure of a computer on a desk, or be integrated into some object,pad, and the like, that is connected to the computer, such as into oneof the computer's USB interfaces. In the example of the source resonatorembedded in the object, pad, and the like, and powered through a USBinterface, the source resonator may then be easily added to a user'sdesktop without the need for being integrated into any other electronicsdevice, thus conveniently providing a wireless energy zone around whicha plurality of electric and/or electronics devices may be powered. Theelectrical facility may be a computer, a light fixture, a dedicatedsource resonator electrical facility, and the like, and the nearbycomponents may be computer peripherals, surrounding electronicscomponents, infrastructure devices, and the like, such as computerkeyboards, computer mouse, fax machine, printer, speaker system, cellphone, audio device, intercom, music player, PDA, lights, electricpencil sharpener, fan, digital picture frame, calculator, electronicgames, and the like. For example, a computer system may be theelectrical facility with an integrated source resonator that utilizes a‘wireless keyboard’ and ‘wireless mouse’, where the use of the termwireless here is meant to indicate that there is wireless communicationfacility between each device and the computer, and where each devicemust still contain a separate battery power source. As a result,batteries would need to be replaced periodically, and in a largecompany, may result in a substantial burden for support personnel forreplacement of batteries, cost of batteries, and proper disposal ofbatteries. Alternatively, the systems and methods described herein mayprovide wireless power transmission from the main body of the computerto each of these peripheral devices, including not only power to thekeyboard and mouse, but to other peripheral components such as a fax,printer, speaker system, and the like, as described herein. A sourceresonator integrated into the electrical facility may provide wirelesspower transmission to a plurality of peripheral devices, user devices,and the like, such that there is a significant reduction in the need tocharge and/or replace batteries for devices in the near vicinity of thesource resonator integrated electrical facility. The electrical facilitymay also provide tuning or auto-tuning software, algorithms, facilities,and the like, for adjusting the power transfer parameters between theelectrical facility and the wirelessly powered device. For example, theelectrical facility may be a computer on a user's desktop, and thesource resonator may be either integrated into the computer or pluggedinto the computer (e.g. through a USB connection), where the computerprovides a facility for providing the tuning algorithm (e.g. through asoftware program running on the computer).

The systems and methods disclosed herein may provide wireless powertransfer to a nearby electrical or electronics component in associationwith a facility infrastructure component, where the source resonator isin, or mounted on, the facility infrastructure component and the deviceresonator is in the electronics component. For instance, the facilityinfrastructure component may be a piece of furniture, a fixed wall, amovable wall or partition, the ceiling, the floor, and the sourceresonator attached or integrated into a table or desk (e.g. justbelow/above the surface, on the side, integrated into a table top ortable leg), a mat placed on the floor (e.g. below a desk, placed on adesk), a mat on the garage floor (e.g. to charge the car and/or devicesin the car), in a parking lot/garage (e.g. on a post near where the caris parked), a television (e.g. for charging a remote control), acomputer monitor (e.g. to power/charge a wireless keyboard, wirelessmouse, cell phone), a chair (e.g. for powering electric blankets,medical devices, personal health monitors), a painting, officefurniture, common household appliances, and the like. For example, thefacility infrastructure component may be a lighting fixture in an officecubical, where the source resonator and light within the lightingfixture are both directly connected to the facility's wired electricalpower. However, with the source resonator now provided in the lightingfixture, there would be no need to have any additional wired connectionsfor those nearby electrical or electronics components that are connectedto, or integrated with, a device resonator. In addition, there may be areduced need for the replacement of batteries for devices with deviceresonators, as described herein.

The use of the systems and methods described herein to supply power toelectrical and electronic devices from a central location, such as froma source resonator in an electrical facility, from a facilityinfrastructure component and the like, may minimize the electricalwiring infrastructure of the surrounding work area. For example, in anenterprise office space there are typically a great number of electricaland electronic devices that need to be powered by wired connections.With utilization of the systems and methods described herein, much ofthis wiring may be eliminated, saving the enterprise the cost ofinstallation, decreasing the physical limitations associated with officewalls having electrical wiring, minimizing the need for power outletsand power strips, and the like. The systems and methods described hereinmay save money for the enterprise through a reduction in electricalinfrastructure associated with installation, re-installation (e.g.,reconfiguring office space), maintenance, and the like. In anotherexample, the principles disclosed herein may allow the wirelessplacement of an electrical outlet in the middle of a room. Here, thesource could be placed on the ceiling of a basement below the locationon the floor above where one desires to put an outlet. The deviceresonator could be placed on the floor of the room right above it.Installing a new lighting fixture (or any other electric device for thatmatter, e.g. camera, sensor, etc., in the center of the ceiling may nowbe substantially easier for the same reason).

In another example, the systems and methods described herein may providepower “through” walls. For instance, suppose one has an electric outletin one room (e.g. on a wall), but one would like to have an outlet inthe next room, but without the need to call an electrician, or drillthrough a wall, or drag a wire around the wall, or the like. Then onemight put a source resonator on the wall in one room, and a deviceresonator outlet/pickup on the other side of the wall. This may power aflat-screen TV or stereo system or the like (e.g. one may not want tohave an ugly wire climbing up the wall in the living room, but doesn'tmind having a similar wire going up the wall in the next room, e.g.storage room or closet, or a room with furniture that blocks view ofwires running along the wall). The systems and methods described hereinmay be used to transfer power from an indoor source to various electricdevices outside of homes or buildings without requiring holes to bedrilled through, or conduits installed in, these outside walls. In thiscase, devices could be wirelessly powered outside the building withoutthe aesthetic or structural damage or risks associated with drillingholes through walls and siding. In addition, the systems and methodsdescribed herein may provide for a placement sensor to assist in placingan interior source resonator for an exterior device resonator equippedelectrical component. For example, a home owner may place a securitylight on the outside of their home which includes a wireless deviceresonator, and now needs to adequately or optimally position the sourceresonator inside the home. A placement sensor acting between the sourceand device resonators may better enable that placement by indicatingwhen placement is good, or to a degree of good, such as in a visualindication, an audio indication, a display indication, and the like. Inanother example, and in a similar way, the systems and methods describedherein may provide for the installation of equipment on the roof of ahome or building, such as radio transmitters and receivers, solar panelsand the like. In the case of the solar panel, the source resonator maybe associated with the panel, and power may be wirelessly transferred toa distribution panel inside the building without the need for drillingthrough the roof. The systems and methods described herein may allow forthe mounting of electric or electrical components across the walls ofvehicles (such as through the roof) without the need to drill holes,such as for automobiles, water craft, planes, trains, and the like. Inthis way, the vehicle's walls may be left intact without holes beingdrilled, thus maintaining the value of the vehicle, maintainingwatertightness, eliminating the need to route wires, and the like. Forexample, mounting a siren or light to the roof of a police car decreasesthe future resale of the car, but with the systems and methods describedherein, any light, horn, siren, and the like, may be attached to theroof without the need to drill a hole.

The systems and methods described herein may be used for wirelesstransfer of power from solar photovoltaic (PV) panels. PV panels withwireless power transfer capability may have several benefits includingsimpler installation, more flexible, reliable, and weatherproof design.Wireless power transfer may be used to transfer power from the PV panelsto a device, house, vehicle, and the like. Solar PV panels may have awireless source resonator allowing the PV panel to directly power adevice that is enabled to receive the wireless power. For example, asolar PV panel may be mounted directly onto the roof of a vehicle,building, and the like. The energy captured by the PV panel may bewirelessly transferred directly to devices inside the vehicle or underthe roof of a building. Devices that have resonators can wirelesslyreceive power from the PV panel. Wireless power transfer from PV panelsmay be used to transfer energy to a resonator that is coupled to thewired electrical system of a house, vehicle, and the like allowingtraditional power distribution and powering of conventional deviceswithout requiring any direct contact between the exterior PV panels andthe internal electrical system.

With wireless power transfer significantly simpler installation ofrooftop PV panels is possible because power may be transmittedwirelessly from the panel to a capture resonator in the house,eliminating all outside wiring, connectors, and conduits, and any holesthrough the roof or walls of the structure. Wireless power transfer usedwith solar cells may have a benefit in that it can reduced roof dangersince it eliminates the need for electricians to work on the roof tointerconnect panels, strings, and junction boxes. Installation of solarpanels integrated with wireless power transfer may require less skilledlabor since fewer electrical contacts need to be made. Less sitespecific design may be required with wireless power transfer since thetechnology gives the installer the ability to individually optimize andposition each solar PV panel, significantly reducing the need forexpensive engineering and panel layout services. There may not be needto carefully balance the solar load on every panel and no need forspecialized DC wiring layout and interconnections.

For rooftop or on-wall installations of PV panels, the capture resonatormay be mounted on the underside of the roof, inside the wall, or in anyother easily accessible inside space within a foot or two of the solarPV panel. A diagram showing a possible general rooftop PV panelinstallation is shown in FIG. 51. Various PV solar collectors may bemounted in top of a roof with wireless power capture coils mountedinside the building under the roof The resonator coils in the PV panelscan transfer their energy wirelessly through the roof to the wirelesscapture coils. The captured energy from the PV cells may be collectedand coupled to the electrical system of the house to power electric andelectronic devices or coupled to the power grid when more power thanneeded is generated. Energy is captured from the PV cells withoutrequiring holes or wires that penetrate the roof or the walls of thebuilding. Each PV panel may have a resonator that is coupled to acorresponding resonator on the interior of the vehicle or building.Multiple panels may utilize wireless power transfer between each otherto transfer or collect power to one or a couple of designated panelsthat are coupled to resonators on the interior of the vehicle of house.Panels may have wireless power resonators on their sides or in theirperimeter that can couple to resonators located in other like panelsallowing transfer of power from panel to panel. An additional bus orconnection structure may be provided that wirelessly couples the powerfrom multiple panels on the exterior of a building or vehicle andtransfers power to one or a more resonators on the interior of buildingor vehicle.

For example, as shown in FIG. 51, a source resonator 5102 may be coupledto a PV cell 5100 mounted on top of roof 5104 of a building. Acorresponding capture resonator 5106 is placed inside the building. Thesolar energy captured by the PV cells can then be transferred betweenthe source resonators 5102 outside to the device resonators 5106 insidethe building without having direct holes and connections through thebuilding.

Each solar PV panel with wireless power transfer may have its owninverter, significantly improving the economics of these solar systemsby individually optimizing the power production efficiency of eachpanel, supporting a mix of panel sizes and types in a singleinstallation, including single panel “pay-as-you-grow” systemexpansions. Reduction of installation costs may make a single paneleconomical for installation. Eliminating the need for panel stringdesigns and careful positioning and orienting of multiple panels, andeliminating a single point of failure for the system.

Wireless power transfer in PV solar panels may enable more solardeployment scenarios because the weather-sealed solar PV panelseliminate the need to drill holes for wiring through sealed surfacessuch as car roofs and ship decks, and eliminate the requirement that thepanels be installed in fixed locations. With wireless power transfer, PVpanels may be deployed temporarily, and then moved or removed, withoutleaving behind permanent alterations to the surrounding structures. Theymay be placed out in a yard on sunny days, and moved around to followthe sun, or brought inside for cleaning or storage, for example. Forbackyard or mobile solar PV applications, an extension cord with awireless energy capture device may be thrown on the ground or placednear the solar unit. The capture extension cord can be completely sealedfrom the elements and electrically isolated, so that it may be used inany indoor or outdoor environment.

With wireless power transfer no wires or external connections may benecessary and the PV solar panels can be completely weather sealed.Significantly improved reliability and lifetime of electrical componentsin the solar PV power generation and transmission circuitry can beexpected since the weather-sealed enclosures can protect components fromUV radiation, humidity, weather, and the like. With wireless powertransfer and weather-sealed enclosures it may be possible to use lessexpensive components since they will no longer be directly exposed toexternal factors and weather elements and it may reduce the cost of PVpanels.

Power transfer between the PV panels and the capture resonators inside abuilding or a vehicle may be bidirectional. Energy may be transmittedfrom the house grid to the PV panels to provide power when the panels donot have enough energy to perform certain tasks such. Reverse power flowcan be used to melt snow from the panels, or power motors that willposition the panels in a more favorable positions with respect to thesun energy. Once the snow is melted or the panels are repositioned andthe PV panels can generate their own energy the direction of powertransfer can be returned to normal delivering power from the PV panelsto buildings, vehicles, or devices.

PV panels with wireless power transfer may include auto-tuning oninstallation to ensure maximum and efficient power transfer to thewireless collector. Variations in roofing materials or variations indistances between the PV panels and the wireless power collector indifferent installations may affect the performance or perturb theproperties of the resonators of the wireless power transfer. To reducethe installation complexity the wireless power transfer components mayinclude a tuning capability to automatically adjust their operatingpoint to compensate for any effects due to materials or distance.Frequency, impedance, capacitance, inductance, duty cycle, voltagelevels and the like may be adjusted to ensure efficient and safe powertransfer

The systems and methods described herein may be used to provide awireless power zone on a temporary basis or in extension of traditionalelectrical outlets to wireless power zones, such as through the use of awireless power extension cord. For example, a wireless power extensioncord may be configured as a plug for connecting into a traditional poweroutlet, a long wire such as in a traditional power extension cord, and aresonant source coil on the other end (e.g. in place of, or in additionto, the traditional socket end of the extension The wireless extensioncord may also be configured where there are source resonators at aplurality of locations along the wireless extension cord. Thisconfiguration may then replace any traditional extension cord wherethere are wireless power configured devices, such as providing wirelesspower to a location where there is no convenient power outlet (e.g. alocation in the living room where there's no outlet), for temporarywireless power where there is no wired power infrastructure (e.g. aconstruction site), out into the yard where there are no outlets (e.g.for parties or for yard grooming equipment that is wirelessly powered todecrease the chances of cutting the traditional electrical cord), andthe like. The wireless extension cord may also be used as a drop withina wall or structure to provide wireless power zones within the vicinityof the drop. For example, a wireless extension cord could be run withina wall of a new or renovated room to provide wireless power zoneswithout the need for the installation of traditional electrical wiringand outlets.

The systems and methods described herein may be utilized to providepower between moving parts or rotating assemblies of a vehicle, a robot,a mechanical device, a wind turbine, or any other type of rotatingdevice or structure with moving parts such as robot arms, constructionvehicles, movable platforms and the like. Traditionally, power in suchsystems may have been provided by slip rings or by rotary joints forexample. Using wireless power transfer as described herein, the designsimplicity, reliability and longevity of these devices may besignificantly improved because power can be transferred over a range ofdistances without any physical connections or contact points that maywear down or out with time. In particular, the preferred coaxial andparallel alignment of the source and device coils may provide wirelesspower transmission that is not severely modulated by the relativerotational motion of the two coils.

The systems and methods described herein may be utilized to extend powerneeds beyond the reach of a single source resonator by providing aseries of source-device-source-device resonators. For instance, supposean existing detached garage has no electrical power and the owner nowwants to install a new power service. However, the owner may not want torun wires all over the garage, or have to break into the walls to wireelectrical outlets throughout the structure. In this instance, the ownermay elect to connect a source resonator to the new power service,enabling wireless power to be supplied to device resonator outletsthroughout the back of the garage. The owner may then install adevice-source ‘relay’ to supply wireless power to device resonatoroutlets in the front of the garage. That is, the power relay may nowreceive wireless power from the primary source resonator, and thensupply available power to a second source resonator to supply power to asecond set of device resonators in the front of the garage. Thisconfiguration may be repeated again and again to extend the effectiverange of the supplied wireless power.

Multiple resonators may be used to extend power needs around an energyblocking material. For instance, it may be desirable to integrate asource resonator into a computer or computer monitor such that theresonator may power devices placed around and especially in front of themonitor or computer such as keyboards, computer mice, telephones, andthe like. Due to aesthetics, space constraints, and the like an energysource that may be used for the source resonator may only be located orconnected to in the back of the monitor or computer. In many designs ofcomputer or monitors metal components and metal containing circuits areused in the design and packaging which may limit and prevent powertransfer from source resonator in the back of the monitor or computer tothe front of the monitor or computer. An additional repeater resonatormay be integrated into the base or pedestal of the monitor or computerthat couples to the source resonator in the back of the monitor orcomputer and allows power transfer to the space in front of the monitoror computer. The intermediate resonator integrated into the base orpedestal of the monitor or computer does not require an additional powersource, it captures power from the source resonator and transfers powerto the front around the blocking or power shielding metal components ofthe monitor or computer.

The systems and methods described herein may be built-into, placed on,hung from, embedded into, integrated into, and the like, the structuralportions of a space, such as a vehicle, office, home, room, building,outdoor structure, road infrastructure, and the like. For instance, oneor more sources may be built into, placed on, hung from, embedded orintegrated into a wall, a ceiling or ceiling panel, a floor, a divider,a doorway, a stairwell, a compartment, a road surface, a sidewalk, aramp, a fence, an exterior structure, and the like. One or more sourcesmay be built into an entity within or around a structure, for instance abed, a desk, a chair, a rug, a mirror, a clock, a display, a television,an electronic device, a counter, a table, a piece of furniture, a pieceof artwork, an enclosure, a compartment, a ceiling panel, a floor ordoor panel, a dashboard, a trunk, a wheel well, a post, a beam, asupport or any like entity. For example, a source resonator may beintegrated into the dashboard of a user's car so that any device that isequipped with or connected to a device resonator may be supplied withpower from the dashboard source resonator. In this way, devices broughtinto or integrated into the car may be constantly charged or poweredwhile in the car.

The systems and methods described herein may provide power through thewalls of vehicles, such as boats, cars, trucks, busses, trains, planes,satellites and the like. For instance, a user may not want to drillthrough the wall of the vehicle in order to provide power to an electricdevice on the outside of the vehicle. A source resonator may be placedinside the vehicle and a device resonator may be placed outside thevehicle (e.g. on the opposite side of a window, wall or structure). Inthis way the user may achieve greater flexibility in optimizing theplacement, positioning and attachment of the external device to thevehicle, (such as without regard to supplying or routing electricalconnections to the device). In addition, with the electrical powersupplied wirelessly, the external device may be sealed such that it iswater tight, making it safe if the electric device is exposed to weather(e.g. rain), or even submerged under water. Similar techniques may beemployed in a variety of applications, such as in charging or poweringhybrid vehicles, navigation and communications equipment, constructionequipment, remote controlled or robotic equipment and the like, whereelectrical risks exist because of exposed conductors. The systems andmethods described herein may provide power through the walls of vacuumchambers or other enclosed spaces such as those used in semiconductorgrowth and processing, material coating systems, aquariums, hazardousmaterials handling systems and the like. Power may be provided totranslation stages, robotic arms, rotating stages, manipulation andcollection devices, cleaning devices and the like.

The systems and methods described herein may provide wireless power to akitchen environment, such as to counter-top appliances, includingmixers, coffee makers, toasters, toaster ovens, grills, griddles,electric skillets, electric pots, electric woks, waffle makers,blenders, food processors, crock pots, warming trays, inductioncooktops, lights, computers, displays, and the like. This technology mayimprove the mobility and/or positioning flexibility of devices, reducethe number of power cords stored on and strewn across the counter-top,improve the washability of the devices, and the like. For example, anelectric skillet may traditionally have separate portions, such as onethat is submersible for washing and one that is not submersible becauseit includes an external electrical connection (e.g. a cord or a socketfor a removable cord). However, with a device resonator integrated intothe unit, all electrical connections may be sealed, and so the entiredevice may now be submersed for cleaning. In addition, the absence of anexternal cord may eliminate the need for an available electrical walloutlet, and there is no longer a need for a power cord to be placedacross the counter or for the location of the electric griddle to belimited to the location of an available electrical wall outlet.

The systems and methods described herein may provide continuouspower/charging to devices equipped with a device resonator because thedevice doesn't leave the proximity of a source resonator, such as fixedelectrical devices, personal computers, intercom systems, securitysystems, household robots, lighting, remote control units, televisions,cordless phones, and the like. For example, a household robot (e.g.ROOMBA) could be powered/charged via wireless power, and thus workarbitrarily long without recharging. In this way, the power supplydesign for the household robot may be changed to take advantage of thiscontinuous source of wireless power, such as to design the robot to onlyuse power from the source resonator without the need for batteries, usepower from the source resonator to recharge the robot's batteries, usethe power from the source resonator to trickle charge the robot'sbatteries, use the power from the source resonator to charge acapacitive energy storage unit, and the like. Similar optimizations ofthe power supplies and power circuits may be enabled, designed, andrealized, for any and all of the devices disclosed herein.

The systems and methods described herein may be able to provide wirelesspower to electrically heated blankets, heating pads/patches, and thelike. These electrically heated devices may find a variety of indoor andoutdoor uses. For example, hand and foot warmers supplied to outdoorworkers such as guards, policemen, construction workers and the likemight be remotely powered from a source resonator associated with orbuilt into a nearby vehicle, building, utility pole, traffic light,portable power unit, and the like.

The systems and methods described herein may be used to power a portableinformation device that contains a device resonator and that may bepowered up when the information device is near an information sourcecontaining a source resonator. For instance, the information device maybe a card (e.g. credit card, smart card, electronic card, and the like)carried in a user's pocket, wallet, purse, vehicle, bike, and the like.The portable information device may be powered up when it is in thevicinity of an information source that then transmits information to theportable information device that may contain electronic logic,electronic processors, memory, a display, an LCD display, LEDs, RFIDtags, and the like. For example, the portable information device may bea credit card with a display that “turns on” when it is near aninformation source, and provide the user with some information such as,“You just received a coupon for 50% off your next Coca Cola purchase”.The information device may store information such as coupon or discountinformation that could be used on subsequent purchases. The portableinformation device may be programmed by the user to contain tasks,calendar appointments, to-do lists, alarms and reminders, and the like.The information device may receive up-to-date price information andinform the user of the location and price of previously selected oridentified items.

The systems and methods described herein may provide wireless powertransmission to directly power or recharge the batteries in sensors,such as environmental sensors, security sensors, agriculture sensors,appliance sensors, food spoilage sensors, power sensors, and the like,which may be mounted internal to a structure, external to a structure,buried underground, installed in walls, and the like. For example, thiscapability may replace the need to dig out old sensors to physicallyreplace the battery, or to bury a new sensor because the old sensor isout of power and no longer operational. These sensors may be charged upperiodically through the use of a portable sensor source resonatorcharging unit. For instance, a truck carrying a source resonatorequipped power source, say providing ˜kW of power, may provide enoughpower to a ˜mW sensor in a few minutes to extend the duration ofoperation of the sensor for more than a year. Sensors may also bedirectly powered, such as powering sensors that are in places where itis difficult to connect to them with a wire but they are still withinthe vicinity of a source resonator, such as devices outside of a house(security camera), on the other side of a wall, on an electric lock on adoor, and the like. In another example, sensors that may need to beotherwise supplied with a wired power connection may be powered throughthe systems and methods described herein. For example, a ground faultinterrupter breaker combines residual current and over-currentprotection in one device for installation into a service panel. However,the sensor traditionally has to be independently wired for power, andthis may complicate the installation. However, with the systems andmethods described herein the sensor may be powered with a deviceresonator, where a single source resonator is provided within theservice panel, thus simplifying the installation and wiringconfiguration within the service panel. In addition, the single sourceresonator may power device resonators mounted on either side of thesource resonator mounted within the service panel, throughout theservice panel, to additional nearby service panels, and the like. Thesystems and methods described herein may be employed to provide wirelesspower to any electrical component associated with electrical panels,electrical rooms, power distribution and the like, such as in electricswitchboards, distribution boards, circuit breakers, transformers,backup batteries, fire alarm control panels, and the like. Through theuse of the systems and methods described herein, it may be easier toinstall, maintain, and modify electrical distribution and protectioncomponents and system installations.

In another example, sensors that are powered by batteries may runcontinuously, without the need to change the batteries, because wirelesspower may be supplied to periodically or continuously recharge ortrickle charge the battery. In such applications, even low levels ofpower may adequately recharge or maintain the charge in batteries,significantly extending their lifetime and usefulness. In some cases,the battery life may be extended to be longer than the lifetime of thedevice it is powering, making it essentially a battery that “lastsforever”.

The systems and methods described herein may be used for chargingimplanted medical device batteries, such as in an artificial heart,pacemaker, heart pump, insulin pump, implanted coils for nerve oracupressure/acupuncture point stimulation, and the like. For instance,it may not be convenient or safe to have wires sticking out of a patientbecause the wires may be a constant source of possible infection and maygenerally be very unpleasant for the patient. The systems and methodsdescribed herein may also be used to charge or power medical devices inor on a patient from an external source, such as from a bed or ahospital wall or ceiling with a source resonator. Such medical devicesmay be easier to attach, read, use and monitor the patient. The systemsand methods described herein may ease the need for attaching wires tothe patient and the patient's bed or bedside, making it more convenientfor the patient to move around and get up out of bed without the risk ofinadvertently disconnecting a medical device. This may, for example, beusefully employed with patients that have multiple sensors monitoringthem, such as for measuring pulse, blood pressure, glucose, and thelike. For medical and monitoring devices that utilize batteries, thebatteries may need to be replaced quite often, perhaps multiple times aweek. This may present risks associated with people forgetting toreplace batteries, not noticing that the devices or monitors are notworking because the batteries have died, infection associated withimproper cleaning of the battery covers and compartments, and the like.

The systems and methods described herein may reduce the risk andcomplexity of medical device implantation procedures. Today manyimplantable medical devices such as ventricular assist devices,pacemakers, defibrillators and the like, require surgical implantationdue to their device form factor, which is heavily influenced by thevolume and shape of the long-life battery that is integrated in thedevice. In one aspect, there is described herein a non-invasive methodof recharging the batteries so that the battery size may be dramaticallyreduced, and the entire device may be implanted, such as via a catheter.A catheter implantable device may include an integrated capture ordevice coil. A catheter implantable capture or device coil may bedesigned so that it may be wired internally, such as after implantation.The capture or device coil may be deployed via a catheter as a rolled upflexible coil (e.g. rolled up like two scrolls, easily unrolledinternally with a simple spreader mechanism). The power source coil maybe worn in a vest or article of clothing that is tailored to fit in sucha way that places the source in proper position, may be placed in achair cushion or bed cushion, may be integrated into a bed or piece offurniture, and the like.

The systems and methods described herein may enable patients to have a‘sensor vest’, sensor patch, and the like, that may include at least oneof a plurality of medical sensors and a device resonator that may bepowered or charged when it is in the vicinity of a source resonator.Traditionally, this type of medical monitoring facility may haverequired batteries, thus making the vest, patch, and the like, heavy,and potentially impractical. But using the principles disclosed herein,no batteries (or a lighter rechargeable battery) may be required, thusmaking such a device more convenient and practical, especially in thecase where such a medical device could be held in place without straps,such as by adhesive, in the absence of batteries or with substantiallylighter batteries. A medical facility may be able to read the sensordata remotely with the aim of anticipating (e.g. a few minutes ahead of)a stroke, a heart-attack, or the like. When the vest is used by a personin a location remote from the medical facility, such as in their home,the vest may then be integrated with a cell-phone or communicationsdevice to call an ambulance in case of an accident or a medical event.The systems and methods described herein may be of particular value inthe instance when the vest is to be used by an elderly person, wheretraditional non-wireless recharging practices (e.g. replacing batteries,plugging in at night, and the like) may not be followed as required. Thesystems and methods described herein may also be used for chargingdevices that are used by or that aid handicapped or disabled people whomay have difficulty replacing or recharging batteries, or reliablysupplying power to devices they enjoy or rely on.

The systems and methods described herein may be used for the chargingand powering of artificial limbs. Artificial limbs have become verycapable in terms of replacing the functionality of original limbs, suchas arms, legs, hands and feet. However, an electrically poweredartificial limb may require substantial power, (such as 10-20 W) whichmay translate into a substantial battery. In that case, the amputee maybe left with a choice between a light battery that doesn't last verylong, and a heavy battery that lasts much longer, but is more difficultto ‘carry’ around. The systems and methods described herein may enablethe artificial limb to be powered with a device resonator, where thesource resonator is either carried by the user and attached to a part ofthe body that may more easily support the weight (such as on a beltaround the waist, for example) or located in an external location wherethe user will spend an adequate amount of time to keep the devicecharged or powered, such as at their desk, in their car, in their bed,and the like.

The systems and methods described herein may be used for charging andpowering of electrically powered exo-skeletons, such as those used inindustrial and military applications, and for elderly/weak/sick people.An electrically powered exo-skeleton may provide up to a 10-to-20 timesincrease in “strength” to a person, enabling the person to performphysically strenuous tasks repeatedly without much fatigue. However,exo-skeletons may require more than 100 W of power under certain usescenarios, so battery powered operation may be limited to 30 minutes orless. The delivery of wireless power as described herein may provide auser of an exo-skeleton with a continuous supply of power both forpowering the structural movements of the exo-skeleton and for poweringvarious monitors and sensors distributed throughout the structure. Forinstance, an exo-skeleton with an embedded device resonator(s) may besupplied with power from a local source resonator. For an industrialexo-skeleton, the source resonator may be placed in the walls of thefacility. For a military exo-skeleton, the source resonator may becarried by an armored vehicle. For an exo-skeleton employed to assist acaretaker of the elderly, the source resonator(s) may be installed orplaced in or the room(s) of a person's home.

The systems and methods described herein may be used for thepowering/charging of portable medical equipment, such as oxygen systems,ventilators, defibrillators, medication pumps, monitors, and equipmentin ambulances or mobile medical units, and the like. Being able totransport a patient from an accident scene to the hospital, or to movepatients in their beds to other rooms or areas, and bring all theequipment that is attached with them and have it powered the whole timeoffers great benefits to the patients' health and eventual well-being.Certainly one can understand the risks and problems caused by medicaldevices that stop working because their battery dies or because theymust be unplugged while a patient is transported or moved in any way.For example, an emergency medical team on the scene of an automotiveaccident might need to utilize portable medical equipment in theemergency care of patients in the field. Such portable medical equipmentmust be properly maintained so that there is sufficient battery life topower the equipment for the duration of the emergency. However, it istoo often the case that the equipment is not properly maintained so thatbatteries are not fully charged and in some cases, necessary equipmentis not available to the first responders. The systems and methodsdescribed herein may provide for wireless power to portable medicalequipment (and associated sensor inputs on the patient) in such a waythat the charging and maintaining of batteries and power packs isprovided automatically and without human intervention. Such a systemalso benefits from the improved mobility of a patient unencumbered by avariety of power cords attached to the many medical monitors and devicesused in their treatment.

The systems and methods described herein may be used to for thepowering/charging of personal hearing aids. Personal hearing aids needto be small and light to fit into or around the ear of a person. Thesize and weight restrictions limit the size of batteries that can beused. Likewise, the size and weight restrictions of the device makebattery replacement difficult due to the delicacy of the components. Thedimensions of the devices and hygiene concerns make it difficult tointegrate additional charging ports to allow recharging of thebatteries. The systems and methods described herein may be integratedinto the hearing aid and may reduce the size of the necessary batterieswhich may allow even smaller hearing aids. Using the principlesdisclosed herein, the batteries of the hearing aid may be rechargedwithout requiring external connections or charging ports. Charging anddevice circuitry and a small rechargeable battery may be integrated intoa form factor of a conventional hearing aid battery allowing retrofitinto existing hearing aids. The hearing aid may be recharged while it isused and worn by a person. The energy source may be integrated into apad or a cup allowing recharging when the hearing is placed on such astructure. The charging source may be integrated into a hearing aiddryer box allowing wireless recharging while the hearing aid is dryingor being sterilized. The source and device resonator may be used to alsoheat the device reducing or eliminating the need for an additionalheating element. Portable charging cases powered by batteries or ACadaptors may be used as storage and charging stations.

The source resonator for the medical systems described above may be inthe main body of some or all of the medical equipment, with deviceresonators on the patient's sensors and devices; the source resonatormay be in the ambulance with device resonators on the patient's sensorsand the main body of some or all of the equipment; a primary sourceresonator may be in the ambulance for transferring wireless power to adevice resonator on the medical equipment while the medical equipment isin the ambulance and a second source resonator is in the main body ofthe medical equipment and a second device resonator on the patientsensors when the equipment is away from the ambulance; and the like. Thesystems and methods described herein may significantly improve the easewith which medical personnel are able to transport patients from onelocation to another, where power wires and the need to replace ormanually charge associated batteries may now be reduced.

The systems and methods described herein may be used for the charging ofdevices inside a military vehicle or facility, such as a tank, armoredcarrier, mobile shelter, and the like. For instance, when soldiers comeback into a vehicle after “action” or a mission, they may typicallystart charging their electronic devices. If their electronic deviceswere equipped with device resonators, and there was a source resonatorinside the vehicle, (e.g. integrated in the seats or on the ceiling ofthe vehicle), their devices would start charging immediately. In fact,the same vehicle could provide power to soldiers/robots (e.g. packbotfrom iRobot) standing outside or walking beside the vehicle. Thiscapability may be useful in minimizing accidental battery-swapping withsomeone else (this may be a significant issue, as soldiers tend to trustonly their own batteries); in enabling quicker exits from a vehicleunder attack; in powering or charging laptops or other electronicdevices inside a tank, as too many wires inside the tank may present ahazard in terms of reduced ability to move around fast in case of“trouble” and/or decreased visibility; and the like. The systems andmethods described herein may provide a significant improvement inassociation with powering portable power equipment in a militaryenvironment.

The systems and methods described herein may provide wireless poweringor charging capabilities to mobile vehicles such as golf carts or othertypes of carts, all-terrain vehicles, electric bikes, scooters, cars,mowers, bobcats and other vehicles typically used for construction andlandscaping and the like. The systems and methods described herein mayprovide wireless powering or charging capabilities to miniature mobilevehicles, such as mini-helicopters, airborne drones, remote controlplanes, remote control boats, remote controlled or robotic rovers,remote controlled or robotic lawn mowers or equipment, bomb detectionrobots, and the like. For instance, mini-helicopter flying above amilitary vehicle to increase its field of view can fly for a few minuteson standard batteries. If these mini-helicopters were fitted with adevice resonator, and the control vehicle had a source resonator, themini-helicopter might be able to fly indefinitely. The systems andmethods described herein may provide an effective alternative torecharging or replacing the batteries for use in miniature mobilevehicles. In addition, the systems and methods described herein mayprovide power/charging to even smaller devices, such asmicroelectromechanical systems (MEMS), nano-robots, nano devices, andthe like. In addition, the systems and methods described herein may beimplemented by installing a source device in a mobile vehicle or flyingdevice to enable it to serve as an in-field or in-flight re-charger,that may position itself autonomously in proximity to a mobile vehiclethat is equipped with a device resonator.

The systems and methods described herein may be used to provide powernetworks for temporary facilities, such as military camps, oil drillingsetups, remote filming locations, and the like, where electrical poweris required, such as for power generators, and where power cables aretypically run around the temporary facility. There are many instanceswhen it is necessary to set up temporary facilities that require power.The systems and methods described herein may enable a more efficient wayto rapidly set up and tear down these facilities, and may reduce thenumber of wires that must be run throughout the faculties to supplypower. For instance, when Special Forces move into an area, they mayerect tents and drag many wires around the camp to provide the requiredelectricity. Instead, the systems and methods described herein mayenable an army vehicle, outfitted with a power supply and a sourceresonator, to park in the center of the camp, and provide all the powerto nearby tents where the device resonator may be integrated into thetents, or some other piece of equipment associated with each tent orarea. A series of source-device-source-device resonators may be used toextend the power to tents that are farther away. That is, the tentsclosest to the vehicle could then provide power to tents behind them.The systems and methods described herein may provide a significantimprovement to the efficiency with which temporary installations may beset up and torn down, thus improving the mobility of the associatedfacility.

The systems and methods described herein may be used in vehicles, suchas for replacing wires, installing new equipment, powering devicesbrought into the vehicle, charging the battery of a vehicle (e.g. for atraditional gas powered engine, for a hybrid car, for an electric car,and the like), powering devices mounted to the interior or exterior ofthe vehicle, powering devices in the vicinity of the vehicle, and thelike. For example, the systems and methods described herein may be usedto replace wires such as those are used to power lights, fans andsensors distributed throughout a vehicle. As an example, a typical carmay have 50 kg of wires associated with it, and the use of the systemsand methods described herein may enable the elimination of a substantialamount of this wiring. The performance of larger and more weightsensitive vehicles such as airplanes or satellites could benefit greatlyfrom having the number of cables that must be run throughout the vehiclereduced. The systems and methods described herein may allow theaccommodation of removable or supplemental portions of a vehicle withelectric and electrical devices without the need for electricalharnessing. For example, a motorcycle may have removable side boxes thatact as a temporary trunk space for when the cyclist is going on a longtrip. These side boxes may have exterior lights, interior lights,sensors, auto equipment, and the like, and if not for being equippedwith the systems and methods described herein might require electricalconnections and harnessing.

An in-vehicle wireless power transmission system may charge or power oneor more mobile devices used in a car: mobile phone handset, Bluetoothheadset, blue tooth hands free speaker phone, GPS, MP3 player, wirelessaudio transceiver for streaming MP3 audio through car stereo via FM,Bluetooth, and the like. The in vehicle wireless power source mayutilize source resonators that are arranged in any of several possibleconfigurations including charging pad on dash, charging pad otherwisemounted on floor, or between seat and center console, charging “cup” orreceptacle that fits in cup holder or on dash, and the like.

The wireless power transmission source may utilize a rechargeablebattery system such that said supply battery gets charged whenever thevehicle power is on such that when the vehicle is turned off thewireless supply can draw power from the supply battery and can continueto wirelessly charge or power mobile devices that are still in the car.

The plug-in electric cars, hybrid cars, and the like, of the future needto be charged, and the user may need to plug in to an electrical supplywhen they get home or to a charging station. Based on a singleover-night recharging, the user may be able to drive up to 50 miles thenext day. Therefore, in the instance of a hybrid car, if a person drivesless than 50 miles on most days, they will be driving mostly onelectricity. However, it would be beneficial if they didn't have toremember to plug in the car at night. That is, it would be nice tosimply drive into a garage, and have the car take care of its owncharging. To this end, a source resonator may be built into the garagefloor and/or garage side-wall, and the device resonator may be builtinto the bottom (or side) of the car. Even a few kW transfer may besufficient to recharge the car over-night. The in-vehicle deviceresonator may measure magnetic field properties to provide feedback toassist in vehicle (or any similar device) alignment to a stationaryresonating source. The vehicle may use this positional feedback toautomatically position itself to achieve optimum alignment, thus optimumpower transmission efficiency. Another method may be to use thepositional feedback to help the human operator to properly position thevehicle or device, such as by making LED's light up, providing noises,and the like when it is well positioned. In such cases where the amountof power being transmitted could present a safety hazard to a person oranimal that intrudes into the active field volume, the source orreceiver device may be equipped with an active light curtain or someother external device capable of sensing intrusion into the active fieldvolume, and capable of shutting off the source device and alert a humanoperator. In addition, the source device may be equipped withself-sensing capability such that it may detect that its expected powertransmission rate has been interrupted by an intruding element, and insuch case shut off the source device and alert a human operator.Physical or mechanical structures such as hinged doors or inflatablebladder shields may be incorporated as a physical barrier to preventunwanted intrusions. Sensors such as optical, magnetic, capacitive,inductive, and the like may also be used to detect foreign structures orinterference between the source and device resonators. The shape of thesource resonator may be shaped such to prevent water or debrisaccumulation. The source resonator may be placed in a cone shapedenclosure or may have an enclosure with an angled top to allow water anddebris to roll off The source of the system may use battery power of thevehicle or its own battery power to transmit its presence to the sourceto initiate power transmission.

The source resonator may be mounted on an embedded or hanging post, on awall, on a stand, and the like for coupling to a device resonatormounted on the bumper, hood, body panel, and the like, of an electricvehicle. The source resonator may be enclosed or embedded into aflexible enclosure such as a pillow, a pad, a bellows, a spring loadedenclosure and the like so that the electric vehicle may make contactwith the structure containing the source coil without damaging the carin any way. The structure containing the source may prevent objects fromgetting between the source and device resonators. Because the wirelesspower transfer may be relatively insensitive to misalignments betweenthe source and device coils, a variety of flexible source structures andparking procedures may be appropriate for this application.

The systems and methods described herein may be used to trickle chargebatteries of electric, hybrid or combustion engine vehicles. Vehiclesmay require small amounts of power to maintain or replenish batterypower. The power may be transferred wirelessly from a source to a deviceresonator that may be incorporated into the front grill, roof, bottom,or other parts of the vehicle. The device resonator may be designed tofit into a shape of a logo on the front of a vehicle or around the grillas not to obstruct air flow through the radiator. The device or sourceresonator may have additional modes of operation that allow theresonator to be used as a heating element which can be used to melt ofsnow or ice from the vehicle.

An electric vehicle or hybrid vehicle may require multiple deviceresonators, such as to increase the ease with which the vehicle may comein proximity with a source resonator for charging (i.e. the greater thenumber and varied position of device resonators are, the greater thechances that the vehicle can pull in and interface with a diversity ofcharging stations), to increase the amount of power that can bedelivered in a period of time (e.g. additional device resonators may berequired to keep the local heating due to charging currents toacceptable levels), to aid in automatic parking/docking the vehicle withthe charging station, and the like. For example, the vehicle may havemultiple resonators (or a single resonator) with a feedback system thatprovides guidance to either the driver or an automated parking/dockingfacility in the parking of the vehicle for optimized charging conditions(i.e., the optimum positioning of the vehicle's device resonator to thecharging station's source resonator may provide greater power transferefficiency). An automated parking/docking facility may allow for theautomatic parking of the vehicle based on how well the vehicle iscoupled.

The power transmission system may be used to power devices andperipherals of a vehicle. Power to peripherals may be provided while avehicle is charging, or while not charging, or power may be delivered toconventional vehicles that do not need charging. For example, power maybe transferred wirelessly to conventional non-electric cars to power airconditioning, refrigeration units, heaters, lights, and the like whileparked to avoid running the engine which may be important to avoidexhaust build up in garage parking lots or loading docks. Power may forexample be wirelessly transferred to a bus while it is parked to allowpowering of lights, peripherals, passenger devices, and the likeavoiding the use of onboard engines or power sources. Power may bewirelessly transferred to an airplane while parked on the tarmac or in ahanger to power instrumentation, climate control, de-icing equipment,and the like without having to use onboard engines or power sources.

Wireless power transmission on vehicles may be used to enable theconcept of Vehicle to Grid (V2G). Vehicle to grid is based on utilizingelectric vehicles and plug-in hybrid electric vehicles (PHEV) asdistributed energy storage devices, charged at night when the electricgrid is underutilized, and available to discharge back into the gridduring episodes of peak demand that occur during the day. The wirelesspower transmission system on a vehicle and the respective infrastructuremay be implemented in such a way as to enable bidirectional energyflow—so that energy can flow back into the grid from the vehicle—withoutrequiring a plug in connection. Vast fleets of vehicles, parked atfactories, offices, parking lots, can be viewed as “peaking powercapacity” by the smart grid. Wireless power transmission on vehicles canmake such a V2G vision a reality. By simplifying the process ofconnecting a vehicle to the grid, (i.e. by simply parking it in awireless charging enabled parking spot), it becomes much more likelythat a certain number of vehicles will be “dispatchable” when the gridneeds to tap their power. Without wireless charging, electric and PHEVowners will likely charge their vehicles at home, and park them at workin conventional parking spots. Who will want to plug their vehicle in atwork, if they do not need charging? With wireless charging systemscapable of handling 3 kW, 100,000 vehicles can provide 300 Megawattsback to the grid—using energy generated the night before by costeffective base load generating capacity. It is the streamlinedergonomics of the cordless self charging PHEV and electric vehicles thatmake it a viable V2G energy source.

The systems and methods described herein may be used to power sensors onthe vehicle, such as sensors in tires to measure air-pressure, or to runperipheral devices in the vehicle, such as cell phones, GPS devices,navigation devices, game players, audio or video players, DVD players,wireless routers, communications equipment, anti-theft devices, radardevices, and the like. For example, source resonators described hereinmay be built into the main compartment of the car in order to supplypower to a variety of devices located both inside and outside of themain compartment of the car. Where the vehicle is a motorcycle or thelike, devices described herein may be integrated into the body of themotorcycle, such as under the seat, and device resonators may beprovided in a user's helmet, such as for communications, entertainment,signaling, and the like, or device resonators may be provided in theuser's jacket, such as for displaying signals to other drivers forsafety, and the like.

The systems and methods described herein may be used in conjunction withtransportation infrastructure, such as roads, trains, planes, shipping,and the like. For example, source resonators may be built into roads,parking lots, rail-lines, and the like. Source resonators may be builtinto traffic lights, signs, and the like. For example, with sourceresonators embedded into a road, and device resonators built intovehicles, the vehicles may be provided power as they drive along theroad or as they are parked in lots or on the side of the road. Thesystems and methods described herein may provide an effective way forelectrical systems in vehicles to be powered and/or charged while thevehicle traverses a road network, or a portion of a road network. Inthis way, the systems and methods described herein may contribute to thepowering/charging of autonomous vehicles, automatic guided vehicles, andthe like. The systems and methods described herein may provide power tovehicles in places where they typically idle or stop, such as in thevicinity of traffic lights or signs, on highway ramps, or in parkinglots.

The systems and methods described herein may be used in an industrialenvironment, such as inside a factory for powering machinery,powering/charging robots, powering and/or charging wireless sensors onrobot arms, powering/charging tools and the like. For example, using thesystems and methods described herein to supply power to devices on thearms of robots may help eliminate direct wire connections across thejoints of the robot arm. In this way, the wearing out of such directwire connections may be reduced, and the reliability of the robotincreased. In this case, the device resonator may be out on the arm ofthe robot, and the source resonator may be at the base of the robot, ina central location near the robot, integrated into the industrialfacility in which the robot is providing service, and the like. The useof the systems and methods described herein may help eliminate wiringotherwise associated with power distribution within the industrialfacility, and thus benefit the overall reliability of the facility.

The systems and methods described herein may be used for undergroundapplications, such as drilling, mining, digging, and the like. Forexample, electrical components and sensors associated with drilling orexcavation may utilize the systems and methods described herein toeliminate cabling associated with a digging mechanism, a drilling bit,and the like, thus eliminating or minimizing cabling near the excavationpoint. In another example, the systems and methods described herein maybe used to provide power to excavation equipment in a mining applicationwhere the power requirements for the equipment may be high and thedistances large, but where there are no people to be subjected to theassociated required fields. For instance, the excavation area may havedevice resonator powered digging equipment that has high powerrequirements and may be digging relatively far from the sourceresonator. As a result the source resonator may need to provide highfield intensities to satisfy these requirements, but personnel are farenough away to be outside these high intensity fields. This high power,no personnel, scenario may be applicable to a plurality of industrialapplications.

The systems and methods described herein may also use the near-fieldnon-radiative resonant scheme for information transfer rather than, orin addition to, power transfer. For instance, information beingtransferred by near-field non-radiative resonance techniques may not besusceptible to eavesdropping and so may provide an increased level ofsecurity compared to traditional wireless communication schemes. Inaddition, information being transferred by near-field non-radiativeresonance techniques may not interfere with the EM radiative spectrumand so may not be a source of EM interference, thereby allowingcommunications in an extended frequency range and well within the limitsset by any regulatory bodies. Communication services may be providedbetween remote, inaccessible or hard-to-reach places such as betweenremote sensors, between sections of a device or vehicle, in tunnels,caves and wells (e.g. oil wells, other drill sites) and betweenunderwater or underground devices, and the like. Communications servicesmay be provided in places where magnetic fields experience less lossthan electric fields.

The systems and methods described herein may enable the simultaneoustransmission of power and communication signals between sources anddevices in wireless power transmission systems, or it may enable thetransmission of power and communication signals during different timeperiods or at different frequencies. The performance characteristics ofthe resonator may be controllably varied to preferentially support orlimit the efficiency or range of either energy or information transfer.The performance characteristics of the resonators may be controlled toimprove the security by reducing the range of information transfer, forexample. The performance characteristics of the resonators may be variedcontinuously, periodically, or according to a predetermined, computed orautomatically adjusted algorithm. For example, the power and informationtransfer enabled by the systems and methods described herein may beprovided in a time multiplexed or frequency multiplexed manner. A sourceand device may signal each other by tuning, changing, varying,dithering, and the like, the resonator impedance which may affect thereflected impedance of other resonators that can be detected. Theinformation transferred as described herein may include informationregarding device identification, device power requirements, handshakingprotocols, and the like.

The source and device may sense, transmit, process and utilize positionand location information on any other sources and/or devices in a powernetwork. The source and device may capture or use information such aselevation, tilt, latitude and longitude, and the like from a variety ofsensors and sources that may be built into the source and device or maybe part of a component the source or device connect. The positioning andorientation information may include sources such as global positioningsensors (GPS), compasses, accelerometers, pressure sensors, atmosphericbarometric sensors, positioning systems which use Wi-Fi or cellularnetwork signals, and the like. The source and device may use theposition and location information to find nearby wireless powertransmission sources. A source may broadcast or communicate with acentral station or database identifying its location. A device mayobtain the source location information from the central station ordatabase or from the local broadcast and guide a user or an operator tothe source with the aid of visual, vibrational, or auditory signals.Sources and devices may be nodes in a power network, in a communicationsnetwork, in a sensor network, in a navigational network, and the like orin kind of combined functionality network.

The position and location information may also be used to optimize orcoordinate power delivery. Additional information about the relativeposition of a source and a device may be used to optimize magnetic fielddirection and resonator alignment. The orientation of a device and asource which may be obtained from accelerometers and magnetic sensors,and the like, for example, may be used to identify the orientation ofresonators and the most favorable direction of a magnetic field suchthat the magnetic flux is not blocked by the device circuitry. With suchinformation a source with the most favorable orientation, or acombination of sources, may be used. Likewise, position and orientationinformation may be used to move or provide feedback to a user oroperator of a device to place a device in a favorable orientation orlocation to maximize power transmission efficiency, minimize losses, andthe like.

The source and device may include power metering and measuring circuitryand capability. The power metering may be used to track how much powerwas delivered to a device or how much power was transferred by a source.The power metering and power usage information may be used in fee basedpower delivery arrangements for billing purposes. Power metering may bealso be used to enable power delivery policies to ensure power isdistributed to multiple devices according to specific criteria. Forexample, the power metering may be used to categorize devices based onthe amount of power they received and priority in power delivery may begiven to those having received the least power. Power metering may beused to provide tiered delivery services such as “guaranteed power” and“best effort power” which may be billed at separate rates. Powermetering may be used to institute and enforce hierarchical powerdelivery structures and may enable priority devices to demand andreceive-more power under certain circumstances or use scenarios.

Power metering may be used to optimize power delivery efficiency andminimize absorption and radiation losses. Information related to thepower received by devices may be used by a source in conjunction withinformation about the power output of the source to identify unfavorableoperating environments or frequencies. For example, a source may comparethe amount of power which was received by the devices and the amount ofpower which it transmitted to determine if the transmission losses maybe unusually or unacceptably large. Large transmission losses may be dueto an unauthorized device receiving power from the source and the sourceand other devices may initiate frequency hopping of the resonancefrequency or other defensive measures to prevent or deter unauthorizeduse. Large transmission losses may be due to absorption losses forexample, and the device and source may tune to alternate resonancefrequencies to minimize such losses. Large transmission losses may alsoindicate the presence of unwanted or unknown objects or materials andthe source may turn down or off its power level until the unwanted orunknown object is removed or identified, at which point the source mayresume powering remote devices.

The source and device may include authentication capability.Authentication may be used to ensure that only compatible sources anddevices are able to transmit and receive power. Authentication may beused to ensure that only authentic devices that are of a specificmanufacturer and not clones or devices and sources from othermanufacturers, or only devices that are part of a specific subscriptionor plan, are able to receive power from a source. Authentication may bebased on cryptographic request and respond protocols or it may be basedon the unique signatures of perturbations of specific devices allowingthem to be used and authenticated based on properties similar tophysically unclonable functions. Authentication may be performed locallybetween each source and device with local communication or it may beused with third person authentication methods where the source anddevice authenticate with communications to a central authority.Authentication protocols may use position information to alert a localsource or sources of a genuine device.

The source and device may use frequency hopping techniques to preventunauthorized use of a wireless power source. The source may continuouslyadjust or change the resonant frequency of power delivery. The changesin frequency may be performed in a pseudorandom or predetermined mannerthat is known, reproducible, or communicated to authorized device butdifficult to predict. The rate of frequency hopping and the number ofvarious frequencies used may be large and frequent enough to ensure thatunauthorized use is difficult or impractical. Frequency hopping may beimplemented by tuning the impedance network, tuning any of the drivingcircuits, using a plurality of resonators tuned or tunable to multipleresonant frequencies, and the like.

The source may have a user notification capability to show the status ofthe source as to whether it is coupled to a device resonator andtransmitting power, if it is in standby mode, or if the source resonatoris detuned or perturbed by an external object. The notificationcapability may include visual, auditory, and vibrational methods. Thenotification may be as simple as three color lights, one for each state,and optionally a speaker to provide notification in case of an error inoperation. Alternatively, the notification capability may involve aninteractive display that shows the status of the source and optionallyprovides instructions on how to fix or solve any errors or problemsidentified.

As another example, wireless power transfer may be used to improve thesafety of electronic explosive detonators. Explosive devices aredetonated with an electronic detonator, electric detonator, or shocktube detonator. The electronic detonator utilizes stored electricalenergy (usually in a capacitor) to activate the igniter charge, with alow energy trigger signal transmitted conductively or by radio. Theelectric detonator utilizes a high energy conductive trigger signal toprovide both the signal and the energy required to activate the ignitercharge. A shock tube sends a controlled explosion through a hollow tubecoated with explosive from the generator to the igniter charge. Thereare safety issues associated with the electric and electronicdetonators, as there are cases of stray electromagnetic energy causingunintended activation. Wireless power transfer via sharply resonantmagnetic coupling can improve the safety of such systems.

Using the wireless power transfer methods disclosed herein, one canbuild an electronic detonation system that has no locally stored energy,thus reducing the risk of unintended activation. A wireless power sourcecan be placed in proximity (within a few meters) of the detonator. Thedetonator can be equipped with a resonant capture coil. The activationenergy can be transferred when the wireless power source has beentriggered. The triggering of the wireless power source can be initiatedby any number of mechanisms: radio, magnetic near field radio,conductive signaling, ultrasonics, laser light. Wireless power transferbased on resonant magnetic coupling also has the benefit of being ableto transfer power through materials such as rock, soil, concrete, water,and other dense materials. The use of very high Q coils as receivers andsources, having very narrow band response and sharply tuned toproprietary frequencies, further ensure that the detonator circuitscannot capture stray EMI and activate unintentionally.

The resonator of a wirelessly powered device may be external, or outsideof the device, and wired to the battery of the device. The battery ofthe device may be modified to include appropriate rectification andcontrol circuitry to receive the alternating currents of the deviceresonator. This can enable configurations with larger external coils,such as might be built into a battery door of a keyboard or mouse, ordigital still camera, or even larger coils that are attached to thedevice but wired back to the battery/converter with ribbon cable. Thebattery door can be modified to provide interconnection from theexternal coil to the battery/converter (which will need an exposedcontact that can touch the battery door contacts.

Stranded Printed Circuit Board Traces

As described in previous sections, high-Q inductive elements in magneticresonators may be formed from litz wire conductors. Litz wires arebundles of thinner, insulated wires woven together in specially designedpatterns so that the thinner individual wires do not occupy the sameradial position within the larger bundle over any significant length.The weave pattern and the use of multiple smaller diameter wireseffectively increases the skin depth and decreases the AC resistance ofthe wire over a range of frequencies.

High-Q inductive elements in magnetic resonators may also be formed fromprinted circuit board (PCB) traces. Printed circuit board traces mayhave a variety of attractive features including accuratereproducibility, easy integration, and cost effective mass-production.In this section, we disclose low AC resistance stranded PCB traces,comprising multiple narrower insulated traces, potentially distributedover multiple board layers, that do not maintain fixed positions withinthe weave pattern, and that may be fabricated using standard fabricationtechniques. The AC resistance of these stranded traces may be determinedby the number, the size, and the relative spacing of the narrowerindividual traces in the designed weave pattern, as well as by thenumber of board layers on which the weave patterns are printed andinterconnected. Individual trace insulation may be provided by air, bycircuit board materials, by coatings, by flexible sheets, by curedmaterials, and the like.

In embodiments, stranded trace weave patterns for PCB fabrication may bedesigned to be easily reproducible and scalable, as well as to achievehigh individual trace densities. The achievable trace density may bedetermined by the narrowness of the individual traces, by the geometryof the weave pattern, and by the need to incorporate other, potentiallylarger structures or features, such as “vias” for example, in the weavepattern. In embodiments, methods and designs that place all the vias orthrough-holes used to connect individual traces between multiple layersof a PCB may be preferably placed on the outer perimeters of themulti-trace weave pattern. The outer location of the vias enables easyscaling and replication of the pattern as well as tight and uniformindividual trace placement and density since the normally larger featuresized vias are not used within the weave pattern itself, potentiallydisrupting the uniformity of the pattern and the density of the weave.

As used in the description of this section, the term ‘stranded trace’means a conductor formed from a group of multiple smaller or narrowerindividual traces, trace segments, or wires. In this section we describetechniques for routing individual traces on a multilayer PCB to formstranded traces that have a lower AC resistance than a solid conductortrace of equivalent size would have.

The braiding of the individual traces on the layered PCB board may beaccomplished by routing each individual trace of a stranded trace in aspecific pattern such that it undulates across and through the variouslayers of the PCB, or otherwise interweaving multiple traces in anoverlapping pattern such as a diagonal mesh or the like across thelayers of the PCB. The weave pattern of the individual traces may bedesigned so that all the individual traces in a stranded trace havesubstantially the same impedance. That is, an alternating currentapplied to the stranded trace will flow in substantially equal amountsin each of the individual traces. Because the current may be distributeduniformly across the strands, the AC resistance may be reduced. Notethat the stranded conductor may be optimally designed for minimizedresistance for specific AC frequencies. In embodiments, systemtrade-offs such as number and size of individual traces, numbers oflayers of the PCB, connection complexities, board space, and the like,may be considered to determine the optimum weave pattern and design.

In this section we may discuss examples which utilize a layered PCBboard with a specific number of layers. The specific number of layers inan example is used to clarify the methods and designs and should not beconsidered as limiting. The methods and designs can be extended andscaled to PCBs with more or fewer layers.

In this section we may discuss and describe examples which refer tospecific layered PCB technologies or implementations. All of thetechniques, methods, algorithms, and implementations described hereinmay be generic and may be applicable to a wide range of layered printedcircuit board technologies and implementations including flex circuitboards and the like.

The method of routing individual traces to form a stranded tracecomprises routing individual traces or segments of traces on differentlayers of a PCB and varying the relative location of each individualtrace or segment within the resulting stranded trace. Each individualtrace of a stranded trace may alter its position on each PCB layer, orthe individual trace may alternate between two or more positions withina pattern on different PCB layers. It may be preferable that eachindividual trace of a stranded trace undulate through all the variouslayers of the layered PCB.

In layered PCB technologies, traces may be routed through to differentconductor or PCB layers with vias or through-holes. The dimensions ofthe vias may be larger than the possible minimum dimensions of theindividual traces, the minimum spacing between individual traces, or theskin depth of AC currents at the frequencies of interest. Inembodiments, the designed weave patterns and routing methods may berealized by placing the vias on the outside edges or the exterior of thestranded traces or weave patterns. In embodiments, it may be possible topack the individual traces as closely as feasible given the fabricationconstraints on the individual traces and trace spacing and still achieveAC resistance values suitable for high-Q inductive elements.

The methods and designs for forming stranded traces on a PCB maycomprise a specific routing of individual conductor traces on each layerand specific routing between each layer of the PCB.

The routing methods and designs may be illustrated and described with anexample shown in FIG. 52 which demonstrates some of the maincharacteristics of the methods and designs. FIG. 52 depicts an exemplaryweave pattern for individual traces that may be formed on each layer ofa four layer printed circuit board. Connecting the individual tracesacross the four layers of the board may form a stranded trace comprisingseven individual traces. These seven individual traces may be arrangedin the pattern shown and may be repeated to the desired length of thestranded trace. The individual traces on each layer are depicted by theblack lines in FIG. 52( a) and the vias are represented by the blackdots on either side of the traces. FIG. 52( a) depicts the individuallayers of conductors side by side for clarity. In a PCB, the four layersare stacked, one on top of the other, and separated by the insulatorlayers of the PCB. A row of vias on a side of the stranded conductor, ormore generally, the area on one or more of the conductor layers boundedby such a row of vias, may be shared by two or more stranded conductors,such as where one of the stranded conductors passes through spacesbetween vias in a row, connects to alternate vias in a row, or in someembodiments, shares vias in a row. It will be appreciated that in thiscontext, a row may also be a vertical row within the PCB, so thatdifferent stranded conductors use a common (vertical) via location toconnect between different conductor layers of the PCB, or pass throughthe via location without connecting to other conductor layers. Thissharing of an area on the PCT may be through (or across) one, some, orall of the layers. For example, the first bottom via 5201 in FIG. 52 isthe same via when the layers are stacked on top of one another. The twonumbers next to each via represent the layers with individual tracesthat are connected by that via. For example, the first bottom via 5201,which is labeled as 4-1 connects the individual trace segments on thefourth conducting layer and the first conducting layer that areconnected to that via.

FIG. 52( b) shows an isometric three dimensional view of the patternfrom FIG. 52( a). Individual traces on each layer are depicted withblack lines and the connections made by the vias between the layers aredepicted with dashed and dotted lines. The four layers of patterns inthis example are stacked on top one another. The spacing and scale ofthe layers, as well as the separation between individual traces on eachlayer have been exaggerated to improve the clarity of the figure. Thevias connect individual trace segments between two layers. In thisexample, all individual trace segments from each layer traverse thewidth of the stranded trace and are routed with the vias to an adjacentlayer.

A stranded trace may be flanked by rows of vias on both sides of theweave pattern. On each PCB layer, the individual traces may traverse thewidth of the effective stranded trace. Each individual trace segment maybe routed from a via on one side of the stranded trace to a via on theother side of the stranded trace. On each PCB layer, each routedindividual trace may be routed from a via that connects that individualtrace to an individual trace on another PCB layer. The individual tracesmay be routed in a manner such that they traverse the width of theeffective stranded trace and also traverse a distance with respect tothe axis of the stranded trace. The axis of the stranded trace is thevirtual line that runs along the length of the stranded trace and isparallel to the rows of vias that flank the stranded trace. The axis ofan exemplary stranded trace is illustrated in FIG. 52( a) with an arrow5203.

In embodiments, each individual trace may be routed in effectively asubstantially diagonal direction with respect to the axis of thestranded trace, where the axis of the stranded trace lies substantiallyparallel to an edge of the PCB. In each conducting layer of the PCB, theindividual traces may be routed in substantially the same direction. Inthe exemplary embodiment of FIGS. 52( a), and 52(b), all the individualtraces of Layer 1 may be routed in a substantially diagonal directionfrom the vias on one side of the stranded trace to the vias on the otherside. Thus, in an arrangement on a PCB having an edge oriented along anx-axis and a y-axis of a plane, the traces may travel diagonally, ormore generally, interconnect vias positioned diagonally with respect toone another within the x-y plane formed by the PCT. Thus, a trace thatis diagonal to an axis of a stranded trace as described herein need notform a straight line, but may be made substantially diagonal with aseries of stair-step lengths that interconnect two diagonally orientedvias. This approximation of a straight-line diagonal permits thefabrication of stranded traces as described herein within the context ofa substantially orthogonal fabrication process such as some commonlyavailable processes for multi-layer PCB manufacturing. At the vias, theindividual traces may be routed to another layer of the PCB. All of theindividual traces from a layer may be routed to another layer, with asimilar, different, translated, reversed and the like, weave pattern atthe vias. On the next layer, the individual traces may again be routed,for example, in a substantially diagonal pattern, from the vias on oneside of the stranded trace to the vias on the other side of the strandedtrace and so on to other layers. This pattern may continue until theindividual traces have traversed all or some of the conducting layers ofthe PCB, whereupon the individual traces may return to the startingconducing layer or an intermediate conducting layer. The individualtraces may undulate in such a manner for any number of cycles, dependingon the weave pattern, the number of conducting layers in the PCB, thedesired length of the stranded trace, and the like. In embodiments, theend points of the stranded traces may be designed to reside of the topand/or bottom layers of the PCBs so they are accessible for easyconnection to other circuit elements or conductors.

In embodiments, on each sequential conductor layer, individual tracesmay be routed in a substantially diagonal direction with respect to theaxis of the stranded trace. In embodiments, on each subsequent conductorlayer, individual conductor traces may be routed in a substantiallyorthogonal direction to that of the previous conductor layer. Thispattern can be seen in FIG. 52( a) and FIG. 52( b). The individualtraces in Layer 1 are routed in a substantially diagonal directiontraversing the stranded trace from left to right in the Figure. In thesubsequent layer, Layer 2, the individual traces are routed in asubstantially diagonal direction that is substantially orthogonal to theconductor traces of Layer 1, and are routed from right to left of thestranded trace.

The routing or path of one individual conductor trace through thevarious conductor layers may be more easily distinguishable in FIG. 53(a), where the path of one of the individual traces is highlighted by adotted black line. Starting with the bottom via 5201, that connectsLayer 4 and Layer 1, the individual trace is routed from the left sideof the stranded trace to a via on the right side that connects Layer 1and Layer 2. In this exemplary embodiment, all the individual traces onLayer 1 are routed from vias that connect Layer 4 and Layer 1 and a viathat connects Layer 1 and Layer 2. The individual trace is routed toLayer 2 by the via and routed right to left in Layer 2 to a via thatconnects Layers 2 and 3. On Layer 2 the individual trace is routed to avia that connects Layers 3 and 4. On Layer 4 the individual trace isrouted to a via that connects Layers 4 and 1, bringing the individualtrace back to the first layer. The pattern can be repeated as many timesas required for a specific length of the stranded trace.

An isometric view of the routing or path of one individual conductortrace through the conductor layers of one example embodiment is depictedin FIG. 53( b). The path of one of the individual traces is highlightedby a thick black line. The individual trace traverses the width of thestranded trace on each layer from one via on one side of the strandedtrace to a via on the other side of the stranded trace. The individualtrace is routed to other layers by the vias. After traversing all of thefour layers the individual trace returns to the starting layer and thepattern continues.

While the example routing patterns shown in FIG. 52 and FIG. 53 feature90 degree angles in the individual traces that form the weave pattern,and is based on a rectilinear routing pattern for the individual traces,various other weave and routing patterns may be used. In exemplaryembodiments, other weave and routing patterns may yield individual tracepatterns that may be along substantially diagonal directions withrespect to the axis of the stranded trace. For example, the individualtraces may bend at shallower angles (such as 45 degrees) to help reducethe gap between traces. In some embodiments, it may be advantageous tomake each individual trace a slanted straight line connected directlybetween two vias. In other embodiments, various curves of the individualtraces may be used when the stranded trace does not follow a straightline path along the circuit board, but turns or loops in a direction,for example. Several alternative exemplary diagonal weave and routingpatterns for individual traces are shown in FIGS. 54( a) and 54(b), butmany other patterns can be derived. In some applications some of thediagonal routing methods may be preferable. For example, for the routingshown in FIG. 54( a), the individual traces are straight lines which maybe preferable because it may result in the shortest overall conductorlength while maintaining consistent spacing between adjacent individualtraces. In embodiments, the weave pattern may differ between some or allof the conductor layers in a PCB. For the exemplary stranded trace shownin FIG. 52, the weave pattern on the even layers differs from the weavepattern on the odd layers. In the exemplary stranded trace shown in FIG.52 the individual traces are routed a distance of four vias in thedirection of the axis of the stranded trace in the odd layers while onlya distance of three vias in the even layers.

As exemplified in FIG. 52, the scheme of the present invention mayconcentrate the vias on either side of the array or group of individualtraces. Thus, the vias (which may have larger minimum feature sizes thantraces and gaps between traces) do not take up space within or betweenthe individual traces. This arrangement of the vias may lead to a higheroverall density of traces and therefore to a lower AC resistance percross-sectional area.

The exemplary routed structures described above can be generalized forstranded traces that comprise a various number of conducting layers of alayered PCB as well as various numbers of individual traces. The generalcharacteristics of the routing method may be characterized by an integerN, representing the number of conductor layers, and an integer M,representing the number of individual conductor traces that make up thestranded trace.

For the designs and methods disclosed here, it may be preferable to havean even number of conductor layers. For some specific weave and routingpatterns vias that connect traces on two layers may be used. A strandedtrace with N conductor layers should have N types of vias connecting thedifferent layers if each via connects only two layers. Each type of viais distinguished or differentiated by the layers that it connects. Ifeach via connects only two layers, for an individual conductor totraverse all of the N layers of a PCB board, there should be N types ofvias in the stranded trace. Preferably, there may be N/2 types of viason either side of the stranded trace, arranged in a fixed repeatingorder. In the exemplary pattern shown in FIG. 52, of the four types ofvias, two types of vias, those that connect Layers 4 and 1 and Layers 2and 3 are located only on one side of the stranded trace while the othertwo types of vias, those that connect Layers 1 and 2 and Layers 3 and 4are located on the other side of the stranded trace. On each layer, anindividual trace may preferably be routed in a substantially diagonaldirection with respect to the axis of the stranded trace such that ithas a displacement of a distance equivalent to at least N/2 vias. Allindividual conducting traces on a layer may have the same displacementin the axis of the stranded trace.

The number of individual traces that make make-up a stranded trace maybe at least partially determined by the total displacement, sometimescharacterized by the number of vias that are passed by, that anindividual trace makes after traveling through all the conductor layersof a PCB. If the displacement, after all the layers have been traversed,is D vias, then the stranded trace may be comprised of up to D/(N/2)individual traces. This relationship can be seen in the example in FIG.53. The individual trace represented by the dotted line is displaced adistance equivalent to 14 vias along the axis of the stranded traceafter traversing through all of the conductor layers. Since the examplehad N=4 layers, the total number of individual conductors that make upthe stranded conductor is M=14/2=7.

A stranded trace can be optimized by considering the number ofindividual traces included in the strand. The larger the number ofindividual traces, the longer each individual trace spends on any onelayer which may reduce the effectiveness of the weaving pattern onreducing skin/proximity effects.

If the number of individual traces and the number of conductor layersare chosen appropriately, it may be possible to ensure that eachindividual trace will be displaced the same distance in each layer alongthe axis of the stranded conductor. A sufficient condition for this tooccur is to choose M(N/2) such that it is divisible by N and to choose Msuch that (M/2)mod(N/2) and N/2 are co-prime where “mod” is the modulooperation.

FIG. 55 shows another example of a partial pattern of weaved individualtraces of the proposed methods. The Figure depicts the individual tracesof the first layer of a ten layer stranded trace design. The ten layerstranded trace consists of 136 separate conductors. The parameters ofthe stranded trace may allow complete symmetry in all ten layers of thestranded conductor. Each conductor layer pattern may be a translatedmirror image of the previous layer. That is, the pattern of traces onodd-numbered layers may be the same pattern as the first layertranslated in such a way that the ends of the individual trace segmentsare connected to the correct vias. The patterns for the even-numberedlayers can be recovered by reflection symmetry and similar translationsfor this example.

FIG. 56 is a cross-sectional view representing the conducting layers ofa multi-layered PCB. The individual trace segments on each layer (notvisible), and therefore the currents they conduct, may flow primarilyinto the page but they have an additional sideways displacement alongeach layer, as indicated by the horizontal arrows in the figure. Thishorizontal displacement enables each trace to move from one side of theweave pattern on a given layer to the opposite side of the weavepattern. Once an individual trace segment reaches the edge of the weavepattern on a particular layer, it is connected by a via (indicated byvertical arrows) to another trace segment on the next layer of the boardand makes its way back across the weave pattern in the oppositedirection. This pattern repeats itself so that each individual tracespends an approximately equal amount of time at each position along thecross-section of the weave pattern. Alternatively, the individual tracesmay be routed between the layers in a non-sequential manner. Anypermutation of the order of layers may be used. It may be preferablethat each individual trace follow the same order or permutation oflayers in a strand of traces. Note that the pattern may be continued byconnecting trace segments on the bottom layer to trace segments on thetop layer, or by routing the traces up and down following the alternatepermutations described above.

Preferably, the cross-sectional dimensions of the individual traces thatmake up the stranded trace on a PCB are small enough (preferably smallerthan one skin-depth δ=√{square root over (2/ωμ_(r)μ₀σ)}) that theyrender the losses induced by one individual trace or segment on itsneighbors small compared to the losses of an isolated individual traceor segment (which for an individual trace smaller than a skin-depth willbe close to the direct current (DC) losses). The braiding of the strandshelps to ensure that all the strands may have substantially the sameimpedance, so that if the same voltage is applied across the bundledstrands (i.e., the strands are driven in parallel), the strands mayindividually conduct substantially the same current. Because the ACcurrent may be distributed uniformly across the strands, the ACresistance may be minimized further.

As an illustration of the above, finite element analysis simulationswere performed on stranded traces made of individual copper traces ofsquare cross-section, driven at 250 kHz. The simulations were performedon stranded traces that have varying aspect ratios as well differentdimensions of the individual conductors. The cross sections of thestranded traces, showing the cross-section of the individual traces ingray are shown in FIG. 58. At this frequency, the skin depth of purecopper is ˜131 μm. If we arrange individual traces that are 152 μm×152μm in cross-section 5801 (a little larger than one skin depth) into asquare array of 8 layers such that the gap between nearest traces bothalong and between the layers is 76 μm as in FIG. 58( a), we find thatthe resistance per meter of a stranded trace conductor braided similarlyto the pattern in FIG. 52 may be 18.7 mΩ/m, which is 64% higher than theDC resistance per length of this structure, 11.4 mΩ/m. By contrast, theresistance per length of this structure if the traces are not braided,or all parallel to the axis of the stranded trace is 31.2 mΩ/m, nearly 3times the DC value.

If we make the individual traces of the stranded trace 76 μm×76 μm incross section 5802 and arrange them into a square array of 16 layerssuch that the gap between traces is 38 μm as in FIG. 58( b) (the overallcross-section being thus essentially unchanged from the previousexample), we find that the AC resistance of a braided structure may be13.2 mΩ/m, about 16% higher than the DC value.

In the case where the cross-sectional dimensions of the traces cannot bemade much smaller than the skin-depth (e.g., because of limitations inmanufacturing), the proximity losses may be reduced by increasing theaspect ratio of the individual traces. The aspect ratio in this contextis the effective width of the stranded conductor on a single tracedivided by the thickness of the stack of conducting and insulatinglayers that make up the stranded trace. In some cases, the thickness ofthe stranded trace is given roughly by the thickness of the PCB.Simulations show that if the aspect ratio of the strand of 152 μm×152 μmtraces described above is changed so that there are twice as many tracesegments on each layer, but half as many layers as depicted in FIG. 58(c), the AC resistance at 250 kHz may be reduced from 18.7 mΩ/m to 16.0mΩ/m. For the structure with 76 μm×76 μm traces, again keeping thenumber of individual conductors the same, but reducing the thickness ofthe structure by a factor of two as depicted in FIG. 58( d) lowers theAC resistance from 13.2 mΩ/m to 12.6 mΩ/m. The DC resistance per lengthin both cases is 11.4 mΩ/m. In embodiments, the preferable aspect ratioof the stranded trace may be application dependent. In embodiments, avariety of factors may be considered in determining the best weavepatterns for specific high-Q inductive element designs. A benefit of theproposed approach is that the vias used in the stranded traces mayperforate the board completely. That is, there is no need for partialvias or buried vias. Using vias that perforate the board completely maysimplify the manufacturing process. For example, several boards can bestacked together and perforated at the same time. Partial vias, or viasthat go through only a few consecutive layers of a PCB typically requireperforation prior to assembly of the individual layers. Likewise, buriedvias, or vias that connect or go through some internal layers of a PCBrequire perforation and preparation prior to assembly of the outerlayers of the PCB during manufacturing. In embodiments, adjacent rows ofvias of adjacent stranded conductors may share the same verticallocation and be stacked one on top of other. In embodiments, adjacentrows of vias of adjacent stranded conductors may be separate and equallyinterspersed.

Another benefit of the methods and designs described herein is that thelocation of vias at the outer edges of the weave pattern may allow forsmaller separations between multi-turn or higher density stranded tracepatterns. When two stranded traces run near each other on a PCB, or whena single stranded trace is shaped, patterned, folded, turned, and/orrouted so that different sections of the stranded trace run near eachother on the PCB, the separation between these traces may be reduced byreusing or interspacing the nearby vias. For example, FIG. 57 shows thetop layer of a PCB with two stranded traces 5701, 5702 that share thesame row of vias wherein, for clarity, the vias of the right strandedtrace 5702 are depicted as white filled circles while the vias of theleft stranded trace 5701 are depicted as black circles. The vias 5703between the two stranded traces 5701, 5702, are all in the same row andthere is substantially no spacing between the two stranded traces.Buried or blind vias, which individually do not traverse or go throughthe whole thickness or all the layers of a PCB, may be stacked on top ofeach other and the density of the routing of the individual conductortraces can be further increased since the spacing between the vias maynot need to be increased to accommodate the vias of an adjacent strandedtrace.

It will be clear to those skilled in the art that many changes andmodifications can be made to the examples shown within the spirit of theinvention. For example, although through vias which perforate the PCBmay be used with the methods, blind vias or buried vias may also beused. It may be possible to have more than one via stacked on top ofanother, and one via location may be used to connect more than two setsof conductor layers together which may be used to increase the densityof the conductor traces in the stranded trace. Likewise, althoughexamples use vias that connected only two board (conductor) layerstogether, the routing method may be modified such that each conductortrace is routed on multiple layers simultaneously. Other modification inthe spirit of the proposed methods may include routing individualconductor traces from one via to multiple vias, routing from multiplevias to one via on each layer, using multiple conductor traces to routefrom one via to another on each conductor layer, or any combinationthereof.

In some embodiments it may be beneficial to misalign the conductortraces between the layers to ensure that the traces all presentsubstantially the same impedance.

The stranded traces may be useful in a large diverse set of applicationsand may serve as a substitute in any application that typically usedtraditional braided litz wire. The stranded trace may be routed in aloop or loops of various shapes and dimensions to create a coil that maybe used in magnetic field power transfer systems such as traditionalinduction based power transfer systems or near-field magnetic resonancepower transfer systems. In some embodiments and applications where thestranded trace may be used as part of a resonator, the trace dimensions,aspect ratio, routing pattern, and the like may be chosen and optimizedto maximize the Q of the resonator. In embodiments, the resonantfrequency of the high-Q resonator may be chosen to take advantage ofspecific weave patterns and/or stranded trace designs.

In embodiments, the PCB stranded trace loops may be routed such that acore of magnetic material may be placed in the middle of the loop tocreate a cored loop. The PCB may have a number of cutouts, channels,pockets, mounts, or holes to accommodate a core.

In embodiments, the PCB of the stranded trace may further be used tocarry and integrate other electronics or electronic components.Electronics to power or drive a resonator formed by the stranded tracemay be located on the same PCB as the traces. While the invention hasbeen described in connection with certain preferred embodiments, otherembodiments will be understood by one of ordinary skill in the art andare intended to fall within the scope of this disclosure, which is to beinterpreted in the broadest sense allowable by law.

All documents referenced herein are hereby incorporated by reference.

What is claimed is:
 1. An inductor, comprising: a plurality of conductorlayers forming a part of a printed circuit board; a plurality ofconductor traces on at least two of the plurality of conductor layers;and a plurality of vias that connect conductor traces on different onesof the plurality of conductor layers, wherein each of the plurality ofconductor traces is characterized by a cross-sectional dimension, andwherein each of the plurality of conductor traces is routed along a pathhaving a substantially similar design, and wherein the path of at leastone of the plurality of conductor traces on one conductor layer islinearly offset from the conductor path it is electrically connected toon at least one other conductor layer and wherein each of the pluralityof conductor traces is formed, at least in part, of conductor material.2. The inductor of claim 1 wherein the conductor traces comprise copper.3. The inductor of claim 1 wherein the conductor traces comprise silver.4. The inductor of claim 1 wherein the conductor traces compriseplatinum.
 5. The inductor of claim 1 wherein the conductor tracecross-sectional dimension is less than 200 micrometers.
 6. The inductorof claim 1 wherein the conductor trace cross-sectional dimension is lessthan 100 micrometers.
 7. The inductor of claim 1 wherein the conductortrace cross-sectional dimension is less than one skin depth of theconductor material at an operating frequency.
 8. The inductor of claim 1wherein the routed path of at least one conductor trace comprises a 90degree bend.
 9. The inductor of claim 1 wherein the path of at least oneconductor trace comprises a bend with an angle less than 90 degrees. 10.The inductor of claim 1 wherein the path of at least one of theplurality of conductor traces comprises an arc.
 11. The inductor ofclaim 1, wherein at least one of the plurality of conductor traces on alayer form a stranded trace.
 12. The inductor of claim 11, wherein theratio of the width of the stranded trace to a thickness of the pluralityof conductor layers that form the inductor is greater than
 1. 13. Theinductor of claim 11, wherein the ratio of the width of the strandedtrace to a thickness of the plurality of conductor layers that form theinductor is greater than
 4. 14. The inductor of claim 11 wherein an ACresistance of the stranded trace is less than twice the DC resistance ofthe stranded trace.
 15. The inductor of claim 1 wherein a magneticmaterial resides within a loop formed by the stranded trace.
 16. Awireless power source comprising: an inductor, comprising: a pluralityof conductor layers forming a part of a printed circuit board; aplurality of conductor traces on at least two of the plurality ofconductor layers; and a plurality of vias that connect conductor traceson different ones of the plurality of conductor layers, wherein each ofthe plurality of conductor traces is characterized by a cross-sectionaldimension, and wherein each of the plurality of conductor traces isrouted along a path having a substantially similar design, and whereinthe path of at least one of the plurality of conductor traces on oneconductor layer is linearly offset from the conductor path it iselectrically connected to on at least one other conductor layer.
 17. Thewireless power source of claim 16, further comprising a power supply.18. The wireless power source of claim 17, wherein the inductor isdriven with a substantially single frequency oscillating drive signal.19. The wireless power source of claim 18, wherein the frequency of thedrive signal is greater than 10 kHz and less than 100 MHz.
 20. Thewireless power source of claim 17, wherein the inductor is driven by awaveform generated in a processor.
 21. The wireless power source ofclaim 16, further comprising at least one high-Q capacitor to form amagnetic resonator.
 22. A wireless power device comprising: an inductor,comprising: a plurality of conductor layers forming a part of a printedcircuit board; a plurality of conductor traces on at least two of theplurality of conductor layers; and a plurality of vias that connectconductor traces on different ones of the plurality of conductor layers,wherein each of the plurality of conductor traces is characterized by across-sectional dimension, and wherein each of the plurality ofconductor traces is routed along a path having a substantially similardesign, and wherein the path of at least one of the plurality ofconductor traces on one conductor layer is linearly offset from theconductor path it is electrically connected to on at least one otherconductor layer.
 23. The wireless power device of claim 22, furthercomprising a rectification circuit.
 24. The wireless power device ofclaim 22, further comprising at least one high-Q capacitor to form amagnetic resonator.
 25. The wireless power device of claim 23, whereinthe output of the rectification circuit supplies power to a device or abattery.